Methane (CH4) behaves as an ideal gas under standard temperature and pressure conditions. What volume is occupied by 1 kg of methane at a temperature of 35 °C and a pressure of 0.9 atm?
Use PV = nRT
You have P, R, T. n = grams/molar mass. Don't forget to convert 35C to kelvin.
To find the volume occupied by 1 kg of methane at the given temperature and pressure, we can use the ideal gas law equation: PV = nRT.
First, we need to convert the given temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is T(K) = T(°C) + 273.15.
T(K) = 35 °C + 273.15 = 308.15 K.
Next, we need to calculate the number of moles of methane. We can use the molar mass of methane to convert the given mass to moles. The molar mass of methane is approximately 16.04 g/mol.
Given mass of methane = 1 kg.
First, we need to convert the mass from kg to grams: 1 kg = 1000 grams.
Number of moles (n) = (mass in grams) / (molar mass).
n = 1000 g / 16.04 g/mol.
n ≈ 62.34 mol.
Now, we have all the necessary parameters to calculate the volume using the ideal gas law equation.
PV = nRT.
V = (nRT) / P.
Plugging in the values, we have:
V = (62.34 mol) * (0.0821 atm·L/mol·K) * (308.15 K) / (0.9 atm).
Simplifying the equation, we get:
V ≈ 1701.52 L.
Therefore, 1 kg of methane at a temperature of 35 °C and a pressure of 0.9 atm occupies approximately 1701.52 liters.