An experiment shows that a 116 mLmL gas sample has a mass of 0.168 gg at a pressure of 697 mmHgmmHg and a temperature of 34 ∘C. What is the molar mass of the gas?
The correct answer and explanation is:
To calculate the molar mass of the gas, we can use the ideal gas law and the definition of molar mass.
Step 1: Use the Ideal Gas Law
PV=nRTPV = nRT
Where:
- PP = pressure in atm
- VV = volume in liters
- nn = number of moles
- RR = 0.0821 L·atm/mol·K
- TT = temperature in Kelvin
Step 2: Convert Given Values
- Volume: 116 mL = 0.116 L
- Mass = 0.168 g
- Pressure: 697 mmHg × (1 atm / 760 mmHg) = 0.9171 atm
- Temperature: 34°C + 273.15 = 307.15 K
Step 3: Solve for Moles Using Ideal Gas Law
n=PVRT=(0.9171)(0.116)(0.0821)(307.15)=0.10638425.218915≈0.00422 moln = \frac{PV}{RT} = \frac{(0.9171)(0.116)}{(0.0821)(307.15)} = \frac{0.106384}{25.218915} ≈ 0.00422 \text{ mol}
Step 4: Calculate Molar Mass
Molar mass=massmoles=0.168 g0.00422 mol≈39.81 g/mol\text{Molar mass} = \frac{\text{mass}}{\text{moles}} = \frac{0.168 \text{ g}}{0.00422 \text{ mol}} ≈ 39.81 \text{ g/mol}
Final Answer:
Molar mass ≈ 39.8 g/mol
Explanation (300 words):
The molar mass of a gas is the mass of one mole of its molecules. To find it, both the mass of a sample and the number of moles it contains must be known. In this case, a gas sample has a volume of 116 mL, a mass of 0.168 g, a pressure of 697 mmHg, and a temperature of 34°C. Using the ideal gas law, one can calculate the number of moles in the sample. Before applying the law, all units must be consistent: pressure must be in atmospheres, volume in liters, and temperature in Kelvin.
Converting the pressure to atmospheres and the volume to liters provides the values needed. The temperature is converted to Kelvin by adding 273.15 to the Celsius temperature. Substituting the converted values into the ideal gas equation allows calculation of the number of moles. This is a key step because it connects the physical conditions of the gas sample to the quantity of gas in moles. Once the number of moles is known, dividing the given mass by the moles gives the molar mass.
The result, approximately 39.8 g/mol, gives the identity of the gas or at least its molecular mass. This method is widely used in chemistry labs to determine unknown gases or verify their purity. It assumes ideal behavior of gases, which is a good approximation under typical laboratory conditions.