A rigid container of nitrogen gas (N2) at 24° C contains 440 L at a pressure of 3.5 atm. If 26.6 kJ of heat are added to the container, what will be the new temperature of the gas?° C
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To determine the new temperature of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature of the gas in Kelvin
First, we need to convert the given temperature from Celsius to Kelvin. The temperature in Kelvin (T) is equal to the temperature in Celsius (°C) plus 273.15:
T = 24°C + 273.15 = 297.15 K
Next, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
We know the pressure (P) is 3.5 atm, the volume (V) is 440 L, and the temperature (T) is 297.15 K. The ideal gas constant (R) is a constant value.
n = (3.5 atm * 440 L) / (0.0821 L·atm/(mol·K) * 297.15 K)
Calculating this expression will give us the number of moles (n) of nitrogen gas present in the container.
Now, we need to calculate the amount of heat added (q) to the system in joules. The relationship between heat (q), number of moles (n), and the molar heat capacity of nitrogen gas (C) is given by the equation:
q = n * C * ΔT
We know the heat added (q) is 26.6 kJ (26.6 * 1000 J), the number of moles (n) is calculated in the previous step, and the molar heat capacity of nitrogen gas (C) is constant. We want to find the change in temperature (ΔT).
Rearranging the equation:
ΔT = q / (n * C)
Now, we can substitute the known values into the equation to find the change in temperature (ΔT).
Finally, we can find the new temperature of the gas by adding the change in temperature (ΔT) to the initial temperature (T).
New temperature = T + ΔT
By following these steps, you can determine the new temperature of the gas in the container.