Question #218709

A sample of 0.623 mol of methane has a volume of 5.0 L at 25 oC. Calculate the pressure of the gas.

Expert's answer

**Q218709**

A sample of 0.623 mol of methane has a volume of 5.0 L at 25^{ o}C. Calculate the pressure of the gas.

**Solution : **

We are given the moles, volume, and temperature of the gas and asked to find the pressure of the gas.

The temperature given in the question is in degree centigrade. Convert it to Kelvin.

moles, n = 0.623 mol

volume, V = 5.0 L

Temperature, T = 25^{ o}C = 25 + 273.15 = 298.15 K.

Gas constant, R = 0.08206 L.atm/mol.K.

Plug all this information in the ideal gas equation, P V = n R T, and find the pressure of the gas.

"P \\ V \\ = \\ n \\ R \\ T"

"P \\ * \\ 5.0 \\ L \\ = \\ 0.0623 \\ mol \\ * \\ 0.08206 \\ L.atm\/mol.K \\ * \\ 298.15 \\ K"

divide both the side by 5.0 L, we have

"\\frac{ P \\ * \\ \\cancel{5.0 \\ L} }{\\cancel{5.0 \\ L }} = \\frac{0.0623 \\ mol \\ * \\ 0.08206 \\ L.atm\/mol.K \\ * \\ 298.15 \\ K }{5.0 \\ L }"

In the question, the quantity with the least number of significant figures is 5.0 L. It is in 2 significant figures, so our final answer must also be in 2 significant figures.

In the correct significant figure, the answer is 3.0 atm.

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