2.9 g of a gas at 95 °C occupied the same volume as 0.184 g of dihydrogen at 17 °C, at the same pressure. What is the molar mass of the gas?

To find the molar mass of the gas in question, we can use the ideal gas law and the concept of molar volume. Since both gases are occupying the same volume under the same pressure, we can relate their amounts using the ideal gas equation. Let's break this down step by step.

Understanding the Ideal Gas Law

The ideal gas law is expressed as:

PV = nRT

Where:

• P = pressure
• V = volume
• n = number of moles
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature in Kelvin

Step 1: Convert Temperatures to Kelvin

We need to convert the temperatures from Celsius to Kelvin:

• For the gas at 95 °C: T1 = 95 + 273.15 = 368.15 K
• For dihydrogen at 17 °C: T2 = 17 + 273.15 = 290.15 K

Step 2: Calculate Moles of Dihydrogen

Next, we calculate the number of moles of dihydrogen (H₂) using its molar mass. The molar mass of dihydrogen is approximately 2 g/mol.

n(H₂) = mass / molar mass = 0.184 g / 2 g/mol = 0.092 moles

Step 3: Relate Moles of Both Gases

Since both gases occupy the same volume and are at the same pressure, we can set up a ratio of their moles:

n(gas) / n(H₂) = T(gas) / T(H₂)

Substituting the known values:

n(gas) / 0.092 = 368.15 / 290.15

Step 4: Solve for Moles of the Gas

Now, we can calculate the moles of the unknown gas:

n(gas) = 0.092 * (368.15 / 290.15)

n(gas) ≈ 0.116 moles

Step 5: Calculate Molar Mass of the Gas

Finally, we can find the molar mass of the gas using the formula:

Molar Mass = mass / moles

Substituting the values:

Molar Mass = 2.9 g / 0.116 moles ≈ 24.83 g/mol

Final Result

The molar mass of the gas is approximately 24.83 g/mol. This calculation shows how we can use the properties of gases and the ideal gas law to determine the molar mass of an unknown substance when compared to a known gas under similar conditions.