If 3.4 mol of methane is heated so that the temperature of the gas increases 45 K while its pressure remains constant, how much heat is added to the gas?

To calculate the amount of heat added to the gas, you can use the formula:

Q = n * C * ΔT

Where:
Q = Heat added (in joules)
n = Number of moles of gas
C = Molar heat capacity of the gas at constant pressure (in joules/mole·K)
ΔT = Change in temperature (in Kelvin)

Let's break down the problem and find the values needed for the formula:

Given:
n = 3.4 mol (number of moles of methane)
ΔT = 45 K (change in temperature)

To calculate the heat added, we need to know the molar heat capacity of methane at constant pressure (C). The molar heat capacity can be found from reference sources or calculated using experimental data. For simplicity, let's assume that the molar heat capacity of methane at constant pressure is 35.3 J/mol·K.

Now, let's plug the values into the formula:

Q = 3.4 mol * 35.3 J/mol·K * 45 K
Q = 5,355.3 J

Therefore, the amount of heat added to the gas is 5,355.3 joules.