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A mass of 1.70 g of an unknown gas exerts a pressure of 0.788 atm at 94 °C in a 1.00-L flask. What is the molar mass of the gas?

(R = 0.08206 L atm/mol K)

A. 16.6 g/mol
B. 38.1 g/mol
C. 22.5 g/mol
D. 65.0 g/mol

Answer :

Final answer:

The molar mass of the gas is 170 g/mol.

Explanation:

To find the molar mass of the gas, we can use the ideal gas law equation:

PV = nRT

Given:

  • Mass of the gas (m) = 1.70 g
  • Pressure (P) = 0.788 atm
  • Volume (V) = 1.00 L
  • Temperature (T) = 94 °C = 94 + 273.15 = 367.15 K
  • Ideal gas constant (R) = 0.08206 L atm/mol K

First, we need to convert the temperature from Celsius to Kelvin by adding 273.15.

Next, we can calculate the number of moles (n) using the rearranged ideal gas law equation:

n = PV / RT

Substituting the given values:

n = (0.788 atm)(1.00 L) / (0.08206 L atm/mol K)(367.15 K)

Simplifying the equation:

n = 0.0100 mol

Finally, we can calculate the molar mass (M) using the formula:

M = m / n

Substituting the given mass and number of moles:

M = 1.70 g / 0.0100 mol

M = 170 g/mol

Therefore, the molar mass of the gas is 170 g/mol.

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