To find the molecular mass of the unknown gas, we will use the Ideal Gas Law and the concept of molar mass. The Ideal Gas Law is given by:

$$PV = nRT$$

Where:

Let's start by converting the temperatures given in degrees Celsius to Kelvin:

According to the problem, the volume and the pressure of both gases are the same. Thus, from the Ideal Gas Law:

$$n_{\text{unknown}} R T_{\text{unknown}} = n_{\text{hydrogen}} R T_{\text{hydrogen}}$$

Since $R$ is constant, it cancels out. Rearranging the equation, we get:

$$n_{\text{unknown}} T_{\text{unknown}} = n_{\text{hydrogen}} T_{\text{hydrogen}}$$

To find the moles of each gas, we use the relation between the mass and the molar mass:

For hydrogen ($H_2$), the molar mass is approximately $2 \, \text{g/mol}$.

$n_{\text{hydrogen}} = \frac{0.368 \, \text{g}}{2 \, \text{g/mol}} = 0.184 \, \text{mol}$

Substituting the values into the equation, we get:

$$\frac{m_{\text{unknown}}}{M_{\text{unknown}}} \times 368.15 \text{ K} = 0.184 \, \text{mol} \times 290.15 \text{ K}$$

Where $m_{\text{unknown}} = 5.8 \, \text{g}$ and $M_{\text{unknown}}$ is the molar mass of the unknown gas which we need to find.

Solving, we have:

$$\frac{5.8}{M_{\text{unknown}}} \times 368.15 = 0.184 \times 290.15$$

$$\frac{5.8 \times 368.15}{M_{\text{unknown}}} = 53.3876$$

$$M_{\text{unknown}} = \frac{5.8 \times 368.15}{53.3876} \approx 40 \, \text{g/mol}$$

Thus, the molecular mass of the unknown gas is approximately 40 g/mol, which corresponds to option (D).

Thermodynamics

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