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ΔH is equal to q when pressure is constant. This can be derived using the equation ΔH=ΔU+PΔV. (q+w) can be substituted for ΔU. (-PexΔV) can then be substituted for w. This results in ΔH=q since -PexΔV cancels out with PΔV as long as P=Pex. I think this condition (P=Pex) may be what was being referred to as nonexpansion in the first response.
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