Search found 62 matches
- Mon Mar 11, 2019 5:55 pm
- Forum: Administrative Questions and Class Announcements
- Topic: Practice Final?
- Replies: 2
- Views: 374
Re: Practice Final?
I haven't seen a practice final on here, but I think Lyndon will post his soon. There is another review for thermochem/dynamics. You can find it if you search "Nathan's Review Session Problems + Solutions"
- Mon Mar 11, 2019 5:49 pm
- Forum: Reaction Mechanisms, Reaction Profiles
- Topic: Rate Law
- Replies: 2
- Views: 312
Re: Rate Law
With elementary steps there's no ambiguity. If the equation is A+A--> B, then you know it requires two moles of A for B to form. If they only give you the overall reaction with no elementary steps, then there could be an intermediate you didn't know about.
- Mon Mar 11, 2019 5:42 pm
- Forum: Ideal Gases
- Topic: Cell Diagram/Ecell
- Replies: 8
- Views: 946
Re: Cell Diagram/Ecell
If you're told the cell does work, cell potential should always be positive. You flip the reduction half reactions and go with whatever gives you the higher voltage. However, if you're not told the cell does work and given a cell diagram, the anode (the species being oxidized) is on the left, and th...
- Mon Mar 04, 2019 5:36 pm
- Forum: Zero Order Reactions
- Topic: Different Orders
- Replies: 5
- Views: 588
Re: Different Orders
Lavelle's outline on his website for chemical kinetics only has the equations listed for zeroth, first, and second order calculations, so I'm assuming this is all we'll need to know for the final. He introduced the idea of higher order reactions, but it is beyond the scope of this class.
- Mon Mar 04, 2019 5:32 pm
- Forum: Method of Initial Rates (To Determine n and k)
- Topic: 7A. 1 in the 7th edition
- Replies: 4
- Views: 391
Re: 7A. 1 in the 7th edition
This question is basically asking you to compare their rates, which can be determined by looking at their stoichiometric coefficients. In this question, you're given the equation A+3B --> 2C. You know that A will be decreasing 3 times slower than B because only one mole of A is decomposing for every...
- Mon Mar 04, 2019 5:24 pm
- Forum: General Rate Laws
- Topic: Rate Law
- Replies: 2
- Views: 313
Re: Rate Law
When it's not clear if the concentration is doubled, then you need to divide one rate law equation by the other, with the respective experimental numbers for each variable. This only works if everything else stays constant besides the one reactant you are working with. You'll end up with a number on...
- Mon Feb 25, 2019 3:40 pm
- Forum: Work, Gibbs Free Energy, Cell (Redox) Potentials
- Topic: DeltaG [ENDORSED]
- Replies: 1
- Views: 296
Re: DeltaG [ENDORSED]
Yes, it shows the relationship between free energy and cell potential.
This equation can be used to show that when E is positive, deltaG will be negative, thus making the reaction spontaneous.
This equation can be used to show that when E is positive, deltaG will be negative, thus making the reaction spontaneous.
- Mon Feb 25, 2019 3:35 pm
- Forum: Appications of the Nernst Equation (e.g., Concentration Cells, Non-Standard Cell Potentials, Calculating Equilibrium Constants and pH)
- Topic: E and Enaught [ENDORSED]
- Replies: 1
- Views: 318
Re: E and Enaught [ENDORSED]
E is the cell potential at any stage of a reaction, so the reaction is not necessarily at equilibrium. E naught is cell potential under standard conditions.
- Mon Feb 25, 2019 3:32 pm
- Forum: Appications of the Nernst Equation (e.g., Concentration Cells, Non-Standard Cell Potentials, Calculating Equilibrium Constants and pH)
- Topic: Nernst equation [ENDORSED]
- Replies: 2
- Views: 472
Re: Nernst equation [ENDORSED]
The Nernst Equation shows us how cell potential is dependent on concentration. We use this equation when we want to calculate the cell potential using the concentration of our reactants and products. Vice versa, we would also be able to calculate the concentration of reactant or product when given t...
- Wed Feb 20, 2019 3:32 pm
- Forum: Galvanic/Voltaic Cells, Calculating Standard Cell Potentials, Cell Diagrams
- Topic: Anode v. Cathode
- Replies: 9
- Views: 986
Re: Anode v. Cathode
It's just convention so people can easily identify the anode and cathode. There's no scientific reason behind it.
- Wed Feb 20, 2019 3:25 pm
- Forum: Gibbs Free Energy Concepts and Calculations
- Topic: 4J3 7th Edition
- Replies: 1
- Views: 200
Re: 4J3 7th Edition
Yes, you use the enthalpy and entropy given in the tables. Check your units. They usually give enthalpy in kJ and entropy in J, so it's possible you forgot to convert.
- Wed Feb 20, 2019 3:14 pm
- Forum: Gibbs Free Energy Concepts and Calculations
- Topic: Spontaneity in the Gibbs Eqn
- Replies: 4
- Views: 453
Re: Spontaneity in the Gibbs Eqn
It will be spontaneous at a low temperature.
- Mon Feb 18, 2019 4:01 pm
- Forum: Phase Changes & Related Calculations
- Topic: Negative and Positive values of delta H and w
- Replies: 6
- Views: 3849
Re: Negative and Positive values of delta H and w
The sign of enthalpy is determined with respect to the system. Therefore, when ΔH is negative, you know heat is decreasing with respect to the system. This is the conventional way of writing signs unless otherwise stated.
- Mon Feb 18, 2019 3:56 pm
- Forum: Student Social/Study Group
- Topic: Best Midterm Review
- Replies: 7
- Views: 768
Re: Best Midterm Review
I highly recommend attending UA sessions since they create worksheets a bit more on the challenging side. Although the worksheets aren't always accurate reflections of the test, you come out with a deeper understanding of the material.
- Mon Feb 18, 2019 3:51 pm
- Forum: Heat Capacities, Calorimeters & Calorimetry Calculations
- Topic: Pressure Change
- Replies: 4
- Views: 475
Re: Pressure Change
It helps to think about it using the ideal gas law, PV=nRT. If moles and temperature remain the same, then you know the entire right hand of the equation is a constant. Say, for example, you increase volume. Then you know since nothing else is changing, pressure has to go down in order for the right...
- Mon Feb 18, 2019 3:44 pm
- Forum: Entropy Changes Due to Changes in Volume and Temperature
- Topic: Entropy change: V, P, T
- Replies: 4
- Views: 2956
Re: Entropy change: V, P, T
ΔS=q/T, so the higher the temperature, the smaller the change in entropy for the same amount of heat released or absorbed. ΔS=nRlnV 2 /V 1 , so if there is a decrease in volume the ln term will become negative, and there will be a decrease in entropy. If volume increases, the ln term becomes positiv...
- Wed Feb 06, 2019 12:27 am
- Forum: Concepts & Calculations Using First Law of Thermodynamics
- Topic: U clarifications
- Replies: 3
- Views: 434
Re: U clarifications
When ΔV=0, ΔU=q+w=q-PΔV. Therefore when we substitute ΔV=0, the term -PΔV turns into zero, and we're left with ΔU=q.
When ΔP=0, then ΔU=qp+w. Heat at a constant pressure is enthalpy, thus the equation will be ΔU=ΔH-PΔV
When ΔP=0, then ΔU=qp+w. Heat at a constant pressure is enthalpy, thus the equation will be ΔU=ΔH-PΔV
- Tue Feb 05, 2019 11:57 pm
- Forum: Heat Capacities, Calorimeters & Calorimetry Calculations
- Topic: thermo equation explanation
- Replies: 4
- Views: 535
Re: thermo equation explanation
The equation ΔS=q/T is applicable to an isothermal, reversible reaction. The other equation ΔS=k B lnW is used to calculate residual entropy, meaning the system is cooled to nearly 0K so molecules are barely moving. We are calculating only the entropy of molecules, not a reaction with heat. A good w...
- Tue Feb 05, 2019 11:46 pm
- Forum: Thermodynamic Definitions (isochoric/isometric, isothermal, isobaric)
- Topic: Monday: Derivation of Isothermal, Reversible Expansion
- Replies: 2
- Views: 428
Re: Monday: Derivation of Isothermal, Reversible Expansion
I don't think it has anything to do with entropy, this is just calculating work with different conditions. The basis of deriving a new equation is due to the slowly decreasing external pressure when the system is expanding. Because P is not constant, we derive a new P by rearranging PV=nRT to P=nRT/...
- Mon Jan 28, 2019 3:23 pm
- Forum: Heat Capacities, Calorimeters & Calorimetry Calculations
- Topic: Extensive vs Intensive properties
- Replies: 4
- Views: 409
Re: Extensive vs Intensive properties
Extensive properties are dependent on the amount of substance, but intensive properties are not. Specific heat capacities are intensive because they're "specific for 1 gram, " while extensive properties would be heat capacities (but not specific to 1 gram of the substance).
- Mon Jan 28, 2019 3:17 pm
- Forum: Reaction Enthalpies (e.g., Using Hess’s Law, Bond Enthalpies, Standard Enthalpies of Formation)
- Topic: Memorizing bond enthalpies
- Replies: 5
- Views: 640
Re: Memorizing bond enthalpies
I'm pretty sure they will give us a table of bond enthalpies if we're required to do those calculations. I would say the only ones you need to know are the basic ones such as C-C bonds, which you'll probably memorize while doing the homework.
- Mon Jan 28, 2019 3:14 pm
- Forum: Phase Changes & Related Calculations
- Topic: Heat Capacity
- Replies: 10
- Views: 961
Re: Heat Capacity
Heat capacity is the amount of energy it takes to raise the temperature of a substance by 1 degree Celsius. Molar heat capacity is the amount of energy it takes to raise the temperature of a substance by 1 degree Celsius per mole of a substance. These two are essentially the same thing, but molar he...
- Wed Jan 23, 2019 2:49 pm
- Forum: Equilibrium Constants & Calculating Concentrations
- Topic: Does [H3O+][OH-] always equal 10^-14?
- Replies: 9
- Views: 1219
Re: Does [H3O+][OH-] always equal 10^-14?
Any time there is a change in temperature then Kw is subject to change. For the purpose of this class we assume Kw=10^-14
- Wed Jan 23, 2019 2:46 pm
- Forum: Equilibrium Constants & Calculating Concentrations
- Topic: Homework: 12.63, 6th edition
- Replies: 2
- Views: 339
Re: Homework: 12.63, 6th edition
When filling out the ICE table, your initial amt. of benzoic acid is .110 M, and the equilibrium concentration of the products (more importantly, equilibrium concentration of H+) is (.024 x .110 M). Since you know [H+], you can find pH. Then set up an equilibrium expression to find K a . It should b...
- Wed Jan 23, 2019 2:34 pm
- Forum: Equilibrium Constants & Calculating Concentrations
- Topic: Specific Notation
- Replies: 5
- Views: 594
Re: Specific Notation
Yes, if you're dealing with a reaction that involves only gases it is more correct to use Pgas, but if you're calculating for a reaction that involves an aqueous solution, you should use hard brackets to indicate Kc.
- Mon Jan 14, 2019 11:45 am
- Forum: Equilibrium Constants & Calculating Concentrations
- Topic: Question 11.7 [ENDORSED]
- Replies: 3
- Views: 353
Re: Question 11.7 [ENDORSED]
Both flask 3 and 4 have the same mole ratios, but I'm assuming they're asking for when the system first reaches equilibrium, which would be flask 3.
- Mon Jan 14, 2019 11:42 am
- Forum: Non-Equilibrium Conditions & The Reaction Quotient
- Topic: homework 11.7 6th edition [ENDORSED]
- Replies: 1
- Views: 314
Re: homework 11.7 6th edition [ENDORSED]
Because they tell you it reaches equilibrium after 54.5% of the molecules dissociate, you can set up an ICE table, with the initial as .1 and the change as -(.545x.1). That will give you the final partial pressure of X2 and you can find the final pressure of 2X by doubling the change of X2 due to th...
- Mon Jan 14, 2019 11:31 am
- Forum: Non-Equilibrium Conditions & The Reaction Quotient
- Topic: 7th Edition 5I.13
- Replies: 1
- Views: 126
Re: 7th Edition 5I.13
Your first term of the equation should be 4X2 rather than 2X2. This is just a mathematical mistake. It should be (2X)2 rather than 2(X)2.
- Wed Jan 09, 2019 4:07 pm
- Forum: Equilibrium Constants & Calculating Concentrations
- Topic: Stability
- Replies: 3
- Views: 303
Re: Stability
Products are not always more stable than reactants. In his example the K value just happened to be large, meaning the reaction favors the products. Reactants can also be more stable than reactants, which would mean a smaller K value.
- Wed Jan 09, 2019 4:01 pm
- Forum: Non-Equilibrium Conditions & The Reaction Quotient
- Topic: example in class
- Replies: 3
- Views: 338
Re: example in class
For this example, the mole ratios of ADP to AD and ADP to Pi are 1, so the change in moles of products is the same as change in moles of reactants. If the mole ratios were different, you would have to multiply by stoichiometric coefficients before finding equilibrium concentrations.
- Wed Jan 09, 2019 3:53 pm
- Forum: Equilibrium Constants & Calculating Concentrations
- Topic: Using Net Ionic Equation
- Replies: 1
- Views: 319
Re: Using Net Ionic Equation
Yes, you have to get rid of spectator ions by writing a net ionic equation first. I'm assuming for this course we only need to identify simple ionic compounds, such as AgCl.
- Sun Dec 02, 2018 2:06 pm
- Forum: Lewis Acids & Bases
- Topic: Identifying Acids and Bases
- Replies: 5
- Views: 749
Re: Identifying Acids and Bases
Compounds that have hydrogen atoms written separately in the formula usually indicate they are the terminal atom and most likely dissociate in water. A good example is CH3COOH. They could have written the compound as CH4COO, but writing it the former way indicates the H is attached at another locati...
- Sun Dec 02, 2018 2:00 pm
- Forum: Administrative Questions and Class Announcements
- Topic: Homework week 10
- Replies: 3
- Views: 428
Re: Homework week 10
Yes, we still have homework due this week in discussion.
- Sun Dec 02, 2018 1:59 pm
- Forum: Lewis Acids & Bases
- Topic: Strong/Weak Acids & Bases
- Replies: 2
- Views: 320
Re: Strong/Weak Acids & Bases
If they give you a table of the dissociation constants, then you can easily determine which ones are stronger or weaker by looking at the numbers.
Generally, you just have to memorize the strong acids, such a H2SO4, HCl, etc.
Generally, you just have to memorize the strong acids, such a H2SO4, HCl, etc.
- Mon Nov 26, 2018 12:10 am
- Forum: Determining Molecular Shape (VSEPR)
- Topic: Homework Help Chapter 4 #5
- Replies: 2
- Views: 318
Re: Homework Help Chapter 4 #5
Maybe there's a typo in the answer key/version you have? I have the 7th ed. and it says the answer is bent.
- Sun Nov 25, 2018 11:40 pm
- Forum: Bond Lengths & Energies
- Topic: Bond Length on test/exam??
- Replies: 1
- Views: 289
Re: Bond Length on test/exam??
Because it's not listed on the Ch4 Outline, I would say we don't need to calculate exact bond lengths for the test. I would check with a TA or Lavelle tomorrow to be sure.
- Sun Nov 25, 2018 11:34 pm
- Forum: Polarisability of Anions, The Polarizing Power of Cations
- Topic: Polarizability
- Replies: 3
- Views: 565
Re: Polarizability
Li+ and Mg2+ have higher polarizabilities, respectively. In (a), both Li+ and Be2+ have the same number of electrons. However, because Be 2+ has more protons, there is a higher nuclear charge, and electrons are drawn in more closely, making the cation smaller and not as likely to lose electrons. Li+...
- Sun Nov 25, 2018 11:13 pm
- Forum: Hybridization
- Topic: Test 3
- Replies: 7
- Views: 897
Re: Test 3
Test 3 begins this week in your discussion. On the website it says the test will cover 2D to 2F, so that would be VSEPR, hybridization, shapes/bond angles, and properties of bonds (eg bond length, polarizability which you can find in 2D).
- Sat Nov 24, 2018 2:47 pm
- Forum: Electronegativity
- Topic: Arrows showing charge
- Replies: 4
- Views: 787
Re: Arrows showing charge
The arrows should point in the direction of the atom with higher electronegativity, indicating an area with higher electron density
- Sat Nov 24, 2018 2:43 pm
- Forum: Lewis Structures
- Topic: Central atoms in Lewis Structure
- Replies: 1
- Views: 312
Re: Central atoms in Lewis Structure
The general rule is that the least electronegative atom is placed in the center. So if you're drawing a Lewis structure that has carbon and oxygen atoms, carbon will be the central atom. However, for elements in row 3 and beyond with available space in the d shell, they can have expanded octets and ...
- Sat Nov 24, 2018 2:37 pm
- Forum: Sigma & Pi Bonds
- Topic: sigma/pi bonds and resonance
- Replies: 1
- Views: 117
Re: sigma/pi bonds and resonance
Yes, I would do that to be safe on a test. If they're resonance structures that have the same number of each type of bond then you could probably say all of them have the same number of pi and sigma bonds.
- Tue Nov 13, 2018 11:31 pm
- Forum: Polarisability of Anions, The Polarizing Power of Cations
- Topic: Determining the polarizability
- Replies: 4
- Views: 563
Re: Determining the polarizability
You generally only consider charge as a factor when the ions are positively charged because that's when atoms are seeking more electrons.
- Tue Nov 13, 2018 11:22 pm
- Forum: Determining Molecular Shape (VSEPR)
- Topic: Remembering
- Replies: 8
- Views: 860
Re: Remembering
It helps if you start by memorizing the basic models where the central atom is bonded to all atoms, such as octahedral. From there, you can replace each bonding atom with lone pairs of electrons and determine the shape. So for an octahedral, you can replace one bonding atom with a lone pair, and tha...
- Tue Nov 13, 2018 11:07 pm
- Forum: Lewis Structures
- Topic: Homework 2.25
- Replies: 2
- Views: 301
Re: Homework 2.25
Yes, you can also think of it in terms of atomic radius. Since phosphorus has more electrons, its electron cloud (and as a result its atomic radius) is larger than nitrogen. Since distance between the two atoms is greater, we know the bond length will also be greater.
- Thu Nov 08, 2018 12:26 am
- Forum: Dipole Moments
- Topic: Dipole-Dipole vs Induced Dipole
- Replies: 5
- Views: 1075
Re: Dipole-Dipole vs Induced Dipole
Dipole-dipole interactions occur between two molecules that already have dipole moments, such as an interaction between 2 HF molecules. In the case of dipole induced dipole, a molecule with a dipole moment will induce a dipole moment in another atom without a dipole moment by distorting its electron...
- Thu Nov 08, 2018 12:20 am
- Forum: Bond Lengths & Energies
- Topic: Bond Length and Bond Strength
- Replies: 5
- Views: 806
Re: Bond Length and Bond Strength
Yes, the more electrons two atoms share, the closer they will be drawn to one another, thus decreasing bond length.
- Thu Nov 08, 2018 12:19 am
- Forum: Polarisability of Anions, The Polarizing Power of Cations
- Topic: Electron distortion
- Replies: 3
- Views: 747
Re: Electron distortion
Larger atoms have more electrons in higher energy levels. As a result, electrons are not bound as tightly to the nucleus and each atom will have a larger electron cloud. Because electrons are loosely attracted to the nucleus, it's easier for them to shift around, so electron clouds are more easily d...
- Fri Nov 02, 2018 9:12 pm
- Forum: Ionic & Covalent Bonds
- Topic: Gallium
- Replies: 3
- Views: 220
Re: Gallium
The most likely charge is 3+ because atoms always try to reach their most stable state. For gallium, it's easier for it to become stable by giving up three electrons rather than receiving 5 electrons to complete its 4p shell. That's why most of the elements on the left side of the periodic table giv...
- Fri Nov 02, 2018 8:44 pm
- Forum: DeBroglie Equation
- Topic: De Broglie Equation
- Replies: 2
- Views: 626
Re: De Broglie Equation
You use De Broglie's equation for everything with mass (electron, proton, everyday objects). You use E=hv for a photon because it has no resting mass.
- Fri Nov 02, 2018 8:37 pm
- Forum: DeBroglie Equation
- Topic: equation definition
- Replies: 5
- Views: 956
Re: equation definition
You use De Broglie's equation for objects with mass. This includes everyday objects, electrons, and protons. You use E=hv when you are doing calculations for a photon since a photon has no resting mass.
- Sun Oct 21, 2018 10:40 pm
- Forum: Heisenberg Indeterminacy (Uncertainty) Equation
- Topic: Problem 1.43
- Replies: 2
- Views: 301
Re: Problem 1.43
You would be solving for the uncertainty in velocity. h is a constant. 350 pm would be delta x, or the uncertainty in position.
- Sun Oct 21, 2018 10:33 pm
- Forum: Properties of Electrons
- Topic: Concept Behind Orbitals
- Replies: 6
- Views: 595
Re: Concept Behind Orbitals
Schrodinger's wave equation gives us electron probability densities, and when we graph them it gives us orbital shapes. However, some orbitals have areas where the electron probability density is zero, meaning you will never find an electron there. This results in a nodal plane that consists of mult...
- Sun Oct 21, 2018 6:20 pm
- Forum: DeBroglie Equation
- Topic: Smallest Detectable Wavelength
- Replies: 2
- Views: 197
Smallest Detectable Wavelength
Does anyone remember what Lavelle said the smallest detectable wavelength is?
- Thu Oct 18, 2018 2:54 am
- Forum: Wave Functions and s-, p-, d-, f- Orbitals
- Topic: Problem 1D 23
- Replies: 2
- Views: 340
Re: Problem 1D 23
To do this we need to know quantum numbers, which is another way to describe orbitals. The variable "n" represents principal energy levels and can take the values of 1,2,3,4,etc. "l" represents subshells (s,p,d,f) and takes the values of 0,1,2,...,n-1. "m" represents or...
- Thu Oct 18, 2018 2:14 am
- Forum: Wave Functions and s-, p-, d-, f- Orbitals
- Topic: Orbitals
- Replies: 3
- Views: 238
Re: Orbitals
Because of the math behind Schrodinger's wave function equation, there are points where the calculated electron probability density is zero, indicating the presence of a nodal plane. The most important thing to know about them is you will never find an electron there. In other orbitals such as dz2 a...
- Thu Oct 18, 2018 1:49 am
- Forum: Einstein Equation
- Topic: Question 1.69 Part B (Sixth Edition)
- Replies: 1
- Views: 254
Re: Question 1.69 Part B (Sixth Edition)
From part (a), you know that the agents should use the low-intensity GaN laser. For part (b), you want to use the equation E photon -work function=E k to find the kinetic energy emitted. Since you know the wavelength, you can use the equation E=hv to find energy per photon. You are given the work fu...
- Thu Oct 11, 2018 10:04 pm
- Forum: Properties of Light
- Topic: Calculate values of n
- Replies: 2
- Views: 183
Re: Calculate values of n
If you look at example 1A.2 in the book, your work process should be exactly like the example but backwards. Because you are given wavelength, you can solve for frequency and plug it back into the Rydberg equation to solve for n₂
- Thu Oct 11, 2018 9:41 pm
- Forum: Photoelectric Effect
- Topic: Photoelectric Effect Equation
- Replies: 3
- Views: 365
Re: Photoelectric Effect Equation
I think Dr. Lavelle explained this using an example of hurdles. If someone doesn't have enough energy, then they will not be able to successfully jump over the hurdle. Similarly, if a photon does not have enough energy, then we say it does not meet the threshold energy, and therefore cannot remove a...
- Thu Oct 11, 2018 9:27 pm
- Forum: Properties of Light
- Topic: HW 1.7 6th Edition Part B
- Replies: 2
- Views: 324
Re: HW 1.7 6th Edition Part B
Same, I solved it and ended up with 150 picometers too.
- Fri Oct 05, 2018 1:37 am
- Forum: Molarity, Solutions, Dilutions
- Topic: Chem 14a Problem G.5
- Replies: 2
- Views: 351
Re: Chem 14a Problem G.5
Hi Nadeen! You can solve these by using the equation M(initial)*V(initial)=M(final)*V(final). This problem is essentially asking you to find the initial volume used to make these dilutions. First, you want to determine what values you are already given. You are given the final number of moles, which...
- Fri Oct 05, 2018 1:20 am
- Forum: Limiting Reactant Calculations
- Topic: Percent Yield
- Replies: 5
- Views: 966
Re: Percent Yield
Your method sounds correct, and the other people who previously answered got 76.5% too. The most likely reason for the difference in percentage is that the book may have used a different molar mass for the compound N2H4.
- Fri Oct 05, 2018 1:06 am
- Forum: Significant Figures
- Topic: sig figs urgent question!
- Replies: 12
- Views: 2202
Re: sig figs urgent question!
Zeros between digits other than zero are always considered significant. The way I like to think of it is that those zeros can't be removed without changing the value of the number.