What is the molar mass of an unknown gas with a density of 2.00 g/l at 1.00 atm and 25.0 °c?

English Chemistry
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what is the molar mass of an unknown gas with a density of 2.00 g/l at 1.00 atm and 25.0 °c?

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Question:
Find the molar mass ((M)) of an unknown gas with a density of 2.00 g/L at 1.00 atm and 25.0 °C.

Solution:
Certainly, here is the answer with mathematical symbols enclosed in dollar signs as requested:

Question:
Find the molar mass M of an unknown gas with a density of 2.00 g/L at 1.00 atm and 25.0 °C.

Solution:
We’ll use the ideal gas law, PV = nRT, to find the molar mass M.

First, we need to convert the temperature to Kelvin:
T = 25.0 + 273.15 = 298.15 \, \text{K}

Now, rearrange the ideal gas law to solve for the number of moles n:
n = \frac{PV}{RT}

Next, find the mass m of the gas using the given density:
D = \frac{m}{V}

Rearrange to solve for mass:
m = D \cdot V

Substitute this expression for mass into the equation for the number of moles:
n = \frac{D \cdot V}{RT}

Now, calculate the number of moles of the gas using the given values:
n = \frac{2.00 \, \text{g/L} \cdot 1.00 \, \text{L}}{0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \cdot 298.15 \, \text{K}}

Simplify this expression:
n = \frac{2.00 \, \text{g}}{0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \cdot 298.15 \, \text{K}}

Calculate the number of moles:
n \approx 0.099 \, \text{mol}

Now, find the molar mass M using the definition of molar mass:
M = \frac{m}{n}

Substitute the mass and moles into this equation:
M = \frac{2.00 \, \text{g}}{0.099 \, \text{mol}}

Calculate the molar mass:
M \approx 20.2 \, \text{g/mol}

So, the molar mass of the unknown gas is approximately 20.2 \, \text{g/mol}.