0.75 mol of argon gas is admitted to an evacuated 40 cm^{3} container at 40 C. The gas then undergoes an isochoric heating to a temperature of 500 C.
What is the final pressure of the gas?(answer in kPa)
pv=nrt
so is it
p*40=.75*r*(40-500),right?
what is r?
R=8.314
you also must convert 40cm^3 to m^3
1m^3= 10^6 cm^3
To find the final pressure of the gas, we can use the ideal gas law equation, which is given as:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature of the gas in Kelvin
Let's break down the given information step by step:
1. The initial conditions are:
- Number of moles of argon gas (n) = 0.75 mol
- Volume of the container (V) = 40 cm^3
2. The gas undergoes an isochoric (constant volume) heating, which means the volume does not change during the process.
3. The final temperature (T) is given as 500 °C. However, we need to convert it to Kelvin by adding 273.15:
- T = 500 + 273.15 = 773.15 K
Now, we can solve for the final pressure (P) using the ideal gas law equation:
PV = nRT
Step 1: Convert the volume from cm^3 to m^3:
- V = 40 cm^3 = 40 × 10^(-6) m^3
Step 2: Substitute the known values into the equation:
- P × V = n × R × T
- P × (40 × 10^(-6)) = (0.75) × (8.314) × (773.15)
Step 3: Rearrange the equation and solve for P:
- P = (0.75 × 8.314 × 773.15) / (40 × 10^(-6))
Calculating the right side of the equation:
- P ≈ 151.067 kPa
Therefore, the final pressure of the gas is approximately 151.067 kPa.