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SOLUTION:

Step 1: List the given values.

[tex]\begin{aligned} & P = \text{678 mmHg = 0.892105 atm} \\ & T = 15^{\circ}\text{C} = \text{288.15 K} \\ & d = \text{1.22 g/L} \end{aligned}[/tex]

Step 2: Calculate the molar mass of a gas.

[tex]\begin{aligned} MM & = \frac{dRT}{P} \\ & = \frac{(\text{1.22 g/L})\left(0.082057 \: \dfrac{\text{L}\cdot\text{atm}}{\text{mol}\cdot\text{K}}\right)(\text{288.15 K})}{\text{0.892105 atm}} \\ & = \boxed{\text{32.335 g/mol}} \end{aligned}[/tex]

Hence, the molar mass of the gas is 32.335 g/mol.

[tex]\\[/tex]

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