A sample of 45.1 g of methane gas (CH4(g)) has a volume of 6.20 L at a pressure of 2.90 atm. Calculate the temperature.
Another one that I'm stumped on, last question for my practice exam, can you explain how to solve?
Use PV = nRT.
You know P, V, R and n.
n = grams/molar mass.
Solve for T (in kelvin).
To solve this problem, you can use the Ideal Gas Law equation:
PV = nRT
where:
P = pressure of the gas (in atm)
V = volume of the gas (in L)
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature of the gas (in Kelvin)
First, you need to calculate the number of moles of methane gas using its molar mass. The molar mass of methane (CH4) is 16.04 g/mol (carbon's atomic mass is 12.01 g/mol and hydrogen's atomic mass is 1.01 g/mol).
molar mass of CH4 = 12.01 g/mol + 4(1.01 g/mol) = 16.04 g/mol
moles of CH4 = mass of CH4 / molar mass of CH4
= 45.1 g / 16.04 g/mol
Now, plug the obtained values into the Ideal Gas Law equation:
(2.90 atm) * (6.20 L) = (moles of CH4) * (0.0821 L·atm/mol·K) * T
Rearrange the equation to solve for T:
T = (P * V) / (n * R)
Substitute the known values:
T = (2.90 atm * 6.20 L) / (moles of CH4 * 0.0821 L·atm/mol·K)
Finally, use the calculated value of moles to find the temperature. Make sure to convert the Celsius temperature to Kelvin by adding 273.15:
T = (2.90 atm * 6.20 L) / ((45.1 g / 16.04 g/mol) * 0.0821 L·atm/mol·K)
Simplify the expression and solve for T to get the temperature in Kelvin.