Question

A sample of the greenhouse gas, methane ( CH4 ) at a pressure of 121.59 kPa, a volume of 31 liters, and a temperature of 360.15 K. How many moles (n) of gas and grams (g) of gas are in the sample

Answer 1

To solve this problem, we can use the ideal gas law, which relates the pressure, volume, temperature, and number of moles of a gas:

PV = nRT

where:
P = pressure (in Pa)
V = volume (in m^3)
n = number of moles
R = universal gas constant (8.31 J/(mol·K))
T = temperature (in K)

First, we need to convert the given pressure, volume, and temperature to SI units:

Pressure = 121.59 kPa = 121.59 x 10^3 Pa
Volume = 31 L = 31 x 10^-3 m^3
Temperature = 360.15 K

Now we can plug in the values and solve for n:

n = (PV) / (RT)
n = (121.59 x 10^3 Pa * 31 x 10^-3 m^3) / (8.31 J/(mol·K) * 360.15 K)
n = 1.48 mol

So the sample contains 1.48 moles of methane.

To find the mass of the gas, we can use the molar mass of methane:

Molar mass of CH4 = 12.01 g/mol (for carbon) + 4 x 1.01 g/mol (for hydrogen) = 16.05 g/mol

Now we can use the formula:

mass = n x M

mass = 1.48 mol x 16.05 g/mol
mass = 23.74 g

So the sample contains 1.48 moles and 23.74 grams of methane.