Question

Question #301e2

Answer 1

The volume of hydrogen is 49 L.

We start with the balanced equation.

`"C" + "2H"_2 → "CH"_4`

Step 1. Calculate the moles of `"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"`