Question

An experiment shows that a 116 ml gas sample has a mass of 0.173 g at a pressure of 721 mmHg and a temperature of 34∘C. What is the molar mass of the gas?

Answer 1

To determine the molar mass of the gas, we convert the given values to standard units, use the ideal gas law to solve for the number of moles, and then divide the mass of the gas by the number of moles.

Step-by-step explanation:

To find the molar mass of the gas, we can use the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, we need to convert the given values to appropriate units: the pressure from mmHg to atm (1 atm = 760 mmHg), the volume from mL to L (1000mL = 1L), and the temperature from degrees Celsius to Kelvin (T(K) = T(°C) + 273.15).

Second, we use the ideal gas law to solve for the number of moles (n).

Next, to find the molar mass (M), we use the equation: M = mass of gas (g) / number of moles (n).

Using the provided data:

- Pressure: P = 721 mmHg = 721 mmHg / 760 mmHg/atm ≈ 0.95 atm

- Volume: V = 116 mL = 116 mL / 1000 mL/L = 0.116 L

- Temperature: T = 34°C = 34 + 273.15 = 307.15 K

- Mass of gas = 0.173 g

So, n = PV / RT = (0.95 atm)(0.116 L) / (0.0821 L∙atm/K∙mol)(307.15 K).

Finally, we calculate M = mass of gas (g) / n.