Question

A cylinder contains 91.9 g of neon (Ne) gas. Another cylinder (twice the volume of the neon cylinder and at the same temperature/pressure), contains hydrogen (H2) gas.

Assuming both are ideal gases, what is the mass of the hydrogen gas (in g)?

Answer 1

Let's use indeal gas law for the first cylinder

$$pV = \frac{{{m_{{\text{Ne}}}}}}{{{M_{{\text{Ne}}}}}}RT$$

where ${{m_{{\text{Ne}}}}}$ - mass of Ne, ${{M_{{\text{Ne}}}}}$ - molar mass of Ne. We know, that pressure and temperature are the same in the second cylinder and ${V_2} = 2V$ , so ideal gas law for the second cylinder will be

$$2pV = \frac{{{m_{{{\text{H}}_2}}}}}{{{M_{{{\text{H}}_2}}}}}RT$$

Thus we can multiply the first equation by 2 and equalize the right sides

$$\frac{{{m_{{{\text{H}}_2}}}}}{{{M_{{{\text{H}}_2}}}}}RT = 2\frac{{{m_{{\text{Ne}}}}}}{{{M_{{\text{Ne}}}}}}RT$$

and express mass of the hydrogen

$${m_{{{\text{H}}_2}}} = 2\frac{{{M_{{{\text{H}}_2}}}}}{{{M_{{\text{Ne}}}}}}{m_{{\text{Ne}}}}$$

Now let's do the calculations (atomic weights can be found in the periodic table so ${M_{{\text{Ne}}}} \approx 20.18[\frac{{\text{g}}}{{{\text{mol}}}}]$ and ${M_{{{\text{H}}_2}}} = 2 \cdot {M_{\text{H}}} \approx 2 \cdot 1.008[\frac{{\text{g}}}{{{\text{mol}}}}] = 2.016[\frac{{\text{g}}}{{{\text{mol}}}}]$ )

$${m_{{{\text{H}}_2}}} = 2\frac{{2.016[\frac{{\text{g}}}{{{\text{mol}}}}]}}{{20.18[\frac{{\text{g}}}{{{\text{mol}}}}]}} \cdot 91.9[{\text{g}}] \approx 18.36[{\text{g}}]$$