High School

A sample of gas has a mass of 38.8 mg. Its volume is 220 mL at a temperature of 57 ∘C and a pressure of 931 torr.

Find the molar mass of the gas.

Answer :

Final Answer:

The molar mass of the gas is approximately 40.06 g/mol.

Explanation:

To find the molar mass of the gas, we can use the ideal gas law, which relates the pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas:

PV = nRT

Where:

P = pressure (in atm)

V = volume (in liters)

n = number of moles

R = ideal gas constant (0.0821 L·atm/(mol·K))

T = temperature (in Kelvin)

First, we need to convert the given values to the appropriate units. The pressure is given in torr, so we convert it to atm:

931 torr * (1 atm / 760 torr) = 1.225 atm

The volume is given in milliliters, so we convert it to liters:

220 mL * (1 L / 1000 mL) = 0.220 L

The temperature is given in Celsius, so we convert it to Kelvin:

57 °C + 273.15 = 330.15 K

Now, we can rearrange the ideal gas law to solve for the number of moles (n):

n = (PV) / (RT)

Plugging in the values:

n = (1.225 atm * 0.220 L) / (0.0821 L·atm/(mol·K) * 330.15 K) ≈ 0.0142 moles

Finally, we can calculate the molar mass by dividing the mass of the gas (38.8 mg) by the number of moles:

Molar mass = (38.8 mg / 0.0142 moles) ≈ 40.06 g/mol

So, the molar mass of the gas is approximately 40.06 g/mol.

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