# Thermochemistry : % Mass Question

#### ElementUser

1. Homework Statement

When a 10.0g sample of a mixture of CH4 and C2H6 is burned in excess oxygen, exactly 525 KJ of heat is produced. What is the percentage by mass of CH4 in the original mixture?

Given: CH4(g) +2 O2(g) -> CO2(g) + 2 H2O(l) $$\Delta$$H= -890.4 KJ

C2H6(g) + $$\frac{7}{2}$$ O2(g) -> 2 CO2(g) + 3 H2O(l) $$\Delta$$H= -1560.0 KJ

2. Homework Equations

N/A

3. The Attempt at a Solution

I take the ratio of the enthalpy of CH4 to C2H6. To do this, I do -890.4/-1560.0. This gives me approx. 0.57 (note that I keep as many digits as possible when doing the actual calculations). Therefore, for every one mol of C2H6 burned, 0.57 mol of CH4 is burned.

I then find out how much of the % of the mixture is burned for the CH4.

$$\frac{0.57}{1.57}$$=36.3%

I proceed to multiply the 525 KJ by this percentage and then convert to grams of CH4 to get 3.44 g of CH4. Finally, I find the % mass by dividing my 3.44 g of CH4 by 10.0g of the original mixture, multiply it by 100% to obtain 34.4% of the original mixture as my final solution.

However, the answer appears to be 17.7%; precisely half of the % mass I acquired. Can someone help point out on what I did wrong?

Any help is appreciated. Thanks in advance~

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#### Borek

Mentor
17.7% doesn't look as a correct answer to me.

#### ElementUser

Hm ok, I was just wondering if there was another method to solve this or if the question's answer was just wrong.

#### Borek

Mentor
There is other method.

You have two unknowns - mass of ethane and mass of methane. Their sum is 10.00. Write other equation for amount of heat produced when you burn the mixture. These are two equations in two unknowns.

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