A container holds 1.1 g of oxygen at a pressure of 7.40 atm .
How much heat is required to increase the temperature by 110 degree C at constant pressure?
How much will the temperature increase if this amount of heat energy is transferred to the gas at constant volume?
To solve these questions, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
1. How much heat is required to increase the temperature by 110 degrees C at constant pressure?
To find the heat required at constant pressure, we need to find the change in temperature and use the equation:
q = nCpΔT
where:
q = heat energy
n = number of moles
Cp = molar heat capacity at constant pressure
ΔT = change in temperature
First, we need to find the number of moles of oxygen. We can use the molar mass of oxygen (32 g/mol) and the given mass of 1.1 g:
n = mass / molar mass
n = 1.1 g / 32 g/mol
Next, we need to find the molar heat capacity at constant pressure for oxygen. The molar heat capacity for oxygen is approximately 29.37 J/(mol*K).
Now we can calculate the heat required:
q = nCpΔT
q = (1.1 g / 32 g/mol) * (29.37 J/(mol*K)) * 110 °C
2. How much will the temperature increase if this amount of heat energy is transferred to the gas at constant volume?
At constant volume, the heat energy is given by the equation:
q = nCvΔT
where:
Cv = molar heat capacity at constant volume
The molar heat capacity at constant volume for oxygen is approximately 20.8 J/(mol*K).
Now we can calculate the temperature increase:
q = nCvΔT
q = (1.1 g / 32 g/mol) * (20.8 J/(mol*K)) * ΔT
Note that in this case, we are solving for ΔT, so we will rearrange the equation:
ΔT = q / (nCv)
And substitute the values accordingly.