Question #301e2

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Answer 1 · 2015-04-19T19:04:14

The volume of hydrogen is 49 L.

We start with the balanced equation.

$C + {2H}_{2} \to {CH}_{4}$ $"C" + "2H"_2 → "CH"_4$

Step 1. Calculate the moles of $C$ $"C"$ .

$36.0 cancel("g C") × "1 mol C"/(12.01 cancel("g C")) = "2.998 mol C"$

Step 2. Calculate the moles of $"H"_2$ .

The balanced equation tells us that 1 mol of $"C"$ reacts with 2 mol of $"H"_2$ . So,

$2.998 cancel("mol C") × ("2 mol H"_2)/(1 cancel("mol C")) = "5.995 mol H"_2$

Step3. To calculate the volume, we use the Ideal Gas Law:

$PV = nRT$

$V = (nRT)/P = (5.995 cancel("mol") × "0.082 06 L"·cancel("atm·K⁻¹mol⁻¹") × 300.0 cancel("K"))/(3.0 cancel("atm")) = "49 L"$