7.9 change in internal energy

[jophan3F]

7.9 A gas in a cylinder was placed in a heater and gained 550 kJ of energy as heat. If the cylinder increased in volume from 345 mL to 1846 mL against an atmospheric pressure of 750. Torr during this process, what is the change in internal energy of the gas in the cylinder?

In the solutions manual, it shows the change in internal energy is (5500 kJ - 0.150 kJ = 5500 kJ). Is the number the same because it was not a significantly large difference?

[Kayla Denton 1A]

Yes, you're right. The number is the same due to sig fig rules: when you add or subtract two numbers, you round your answer to the least number of decimal places present in the numbers you are adding or subtracting. Since 5500 has 0 decimal places, you round your answer to the nearest whole number.

[Jennifer Aguayo 1I]

For the pressure, how do we convert torr to atm?
In the solutions manual they divided 750torr by 760 torr x atm^-1 But how do we know it is 760, is that given to us or do we just have to know it? I cannot find it in the equation sheet.

[Niharika Reddy 1D]

The conversion factor (760 torr=1 atm) would be given to us.

Although the back of the periodic table doesn't explicitly state that conversion factor, it gives the gas constant in L·atm/K·mol (.08206) and in L·torr/K·mol (62.364). Since we want the conversion factor of torr to atm, we can get that by dividing the second equivalent of the gas constant listed above by the first. (62.364/0.08206=759.98~760 torr/atm, or 760 torr=1 atm)