SHOW WORK
A 44g sample of CO2 has a volume of 22.4 L at STP. The sample is heated to 71 degrees Celsius and compressed to a volume of 18.0 L. What is the resulting pressure?
Use PV = nRT first and the STP conditions to determine n = numberr of mols.
Then use PV = nRT and solve for P under the new conditions and n from the first part of the problem.
To solve this problem, we need to apply the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure in Pascals (Pa)
V = volume in cubic meters (m^3)
n = number of moles of gas
R = ideal gas constant = 8.314 J/(mol·K)
T = temperature in Kelvin (K)
First, let's convert the given temperature from Celsius to Kelvin:
T = 71°C + 273.15 = 344.15 K
Now, let's calculate the initial number of moles of CO2 using its molar mass (44 g) and its sample mass (44 g):
n₁ = m₁ / M
n₁ = 44 g / 44.01 g/mol ≈ 0.999 mol
Next, we can calculate the initial pressure (P₁) at STP (Standard Temperature and Pressure), which is 1 atmosphere (atm) or 101.325 kilopascals (kPa):
P₁ = 101.325 kPa = 101,325 Pa
Using the ideal gas law equation at STP, we can find the initial volume (V₁):
P₁V₁ = n₁RT
V₁ = n₁RT₁ / P₁
V₁ = (0.999 mol) (8.314 J/(mol·K)) (273.15 K) / 101,325 Pa ≈ 0.0224 m³
Now, we can use the combined gas law equation to find the resulting pressure (P₂):
P₁V₁ / T₁ = P₂V₂ / T₂
Rearranging the equation to solve for P₂:
P₂ = (P₁V₁T₂) / (V₂T₁)
Substituting the given values:
P₂ = (101,325 Pa) (0.0224 m³) (344.15 K) / (18.0 L) (273.15 K)
Converting the units to match:
P₂ = (101,325 Pa) (0.0224 m³) (344.15 K) / (18.0 L) (273.15 K) (1000 L / 1 m³)
Simplifying and solving:
P₂ ≈ 226,970 Pa
Therefore, the resulting pressure of the CO2 sample after being heated and compressed is approximately 226,970 Pa.