Chemistry Daily Challenge 15-July-2015

Chemistry Level 4

A $32 \text{ g}$ sample of $\ce{CH_4}$ gas initially at $101.325 \text{ kPa}$ and $300 \text{ K}$ was heated to $550 K$ . $C_p$ in SI units is

$C_p=12.552+8.368\times10^{-2} T$

Compute $\Delta H$ in Joules.

The answer is 24058.

2 solutions

Aamir Faisal Ansari
Jul 24, 2015

We know $H=U-PV$ $\Delta H=\Delta U-\Delta (PV)$ At constant pressure $\Delta H=\Delta U-P\Delta V$ First law of thermodynamics: $Q=\Delta U-P\Delta V$ Hence $\Delta H=Q=n\int_{T_1}^{T_2} C_p \: dT$ where $n$ is number of mole of methane. Since $\quad n=\frac{32}{16}=2 \space\text{ mol}$ , we have

$\Delta H=2 \times \int_{300\text{ K}}^{550\text{ K}} {(12.552+8.368\times 10^{-2}T) \: dT}$

$\Delta H =24058\text{ J}.$

There's a little problem in the solution. In the question, in Cp 'T' is outside the brackets and while integrating you have used T with 8.368*10 power -2. Please review the question and solution.

Sahil Bansal - 5 years, 5 months ago

In future, if you spot any errors with a problem, you can “report” it by selecting "report problem" in the “More” menu in the top right corner. This will notify the problem creator who can fix the issues.

Calvin Lin Staff - 5 years, 4 months ago

Good Problem ! . Slight More Variation Can Be Made By Giving A Relation between P And V And Then Find The Heat Capacity Of Gas

Prakhar Bindal - 5 years, 7 months ago

The T is outside of the parentheses.

Michelle Valdez - 5 years, 4 months ago

@Aamir Faisal Ansari check the 2nd last step in solution. You have taken T inside the parentheses. @Michelle Valdez

Sahil Bansal - 5 years, 4 months ago

Yes i think someone has unintentionally editted the problem. when i solved it T was inside the bracket only . thats why i got it correct :)

Prakhar Bindal - 5 years, 4 months ago

Calvin Lin Staff - 5 years, 4 months ago

Spandan Senapati
Feb 27, 2017

Use Kirchoff's Law(That's essentially nothing but $dH=nCpdT$ ).Then integrate under suitable limits $(T1=300K to T2=550K)$

Chemistry Daily Challenge 15-July-2015

The answer is 24058.

2 solutions

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