If 28.0 g of methane gas (#CH_4#) are introduced into an evacuated 2.00-L gas cylinder at a temperature of 35°C, what is the pressure inside the cylinder?

Question

Ellie Andrews · Accepted Answer

The pressure of the methane gas will be 22.2 atm.

Use the ideal gas law with the formula #PV=nRT#, where #n# is moles, #R# is the gas constant, and #T# is temperature in Kelvins. Determine the mole of #"CH"_4"# by dividing the given mass by its molar mass, #"16.04246 g/mol"# https://tutor.hix.ai #28.0cancel"g CH"_4xx(1"mol CH"_4)/(16.04246cancel"g CH"_4)="1.7454 mol CH"_4"# Perfect Gas Law Given/Known #V="2.00 L"# #n="1.7454 mol"# #R="0.082057338 L atm K"^(-1) "mol"^(-1)# #T="35"^@"C"+273.15="308 K"# Unknown Pressure, #P# Solution Rearrange the formula to isolate #P#. Substitute the given values into the formula and solve. #PV=nRT# #P=(nRT)/V# #P=((1.7454"mol") xx (0.082057338"L atm K"^(-1) "mol"^(-1)) xx (308"K"))/(2.00"L")="22.2 atm"# rounded to three significant figures

Luna Chen · Answer

undefined Using the ideal gas law equation $PV = nRT$, where $P$ is the pressure, $V$ is the volume, $n$ is the number of moles, $R$ is the ideal gas constant, and $T$ is the temperature in Kelvin, we can solve for pressure. First, we need to calculate the number of moles of methane using its molar mass and then convert the temperature to Kelvin. Finally, we can rearrange the equation to solve for pressure:

$$n = \frac{28.0 \, \text{g}}{16.04 \, \text{g/mol}} = 1.744 \, \text{mol}$$
$$T = 35°C + 273.15 = 308.15 \, \text{K}$$

$$P = \frac{nRT}{V} = \frac{(1.744 \, \text{mol})(0.08206 \, \text{atm} \cdot \text{L/mol} \cdot \text{K})(308.15 \, \text{K})}{2.00 \, \text{L}} = 21.6 \, \text{atm}$$