Calculating the Molar Mass of a Gas Using Ideal Gas Law

What is the molar mass of a 10.21 grams of a gas that has a pressure of 5.48 atm, a volume of 849 mL and a temperature of 25°C?

Final answer: The molar mass of the gas is calculated using the Ideal Gas Law. After converting all the measurements to the appropriate units and rearranging the formula to solve for moles, the molar mass is found to be approximately 43.08 g/mol.

Explanation: In this question, we are asked to find the molar mass of a gas. The molar mass can be calculated using the ideal gas law, which is PV=nRT. For the ideal gas law, P represents the pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. First, convert the temperature from Celsius to Kelvin by adding 273 to 25°C, which gives us 298K. The volume needs to be converted from mL to L, so 849mL equal to 0.849L. Given that the pressure is 5.48 atm and we'll use the gas constant R as 0.0821 L·atm/K·mol.

Re-arranging the ideal gas law equation to solve for n (moles), we get n=PV/RT. Substituting the values in, we have: n = (5.48 atm * 0.849 L) / (0.0821 L·atm/K·mol * 298 K) = 0.237 mol.

The last step is to calculate the molar mass. The molar mass is the mass of the sample divided by the number of moles. That gives us (10.21 g / 0.237 mol) which equals approximately 43.08 g/mol. Therefore, the molar mass of the gas is 43.08 g/mol.

Question:

How do you calculate the molar mass of a gas using the Ideal Gas Law?

Answer:

To calculate the molar mass of a gas using the Ideal Gas Law, you need to know the pressure, volume, temperature, and mass of the gas sample. Start by converting all units to the appropriate form (e.g., pressure to atm, volume to liters, temperature to Kelvin). Then, rearrange the Ideal Gas Law equation PV=nRT to solve for moles (n). Finally, divide the mass of the gas sample by the number of moles to find the molar mass in grams per mole. In this case, the molar mass is approximately 43.08 g/mol.