An ideal gas is contained in a cylinder with a volume of 5.0 102 mL at a temperature of 30.°C and a pressure of 710. torr. The gas is then compressed to a volume of 27 mL, and the temperature is raised to 800.°C. What is the new pressure of the gas?
see above response by Bob Pursley.
To find the new pressure of the gas, we can use the combined gas law equation:
(P₁ × V₁) / (T₁) = (P₂ × V₂) / (T₂)
Where:
P₁ = initial pressure of the gas
V₁ = initial volume of the gas
T₁ = initial temperature of the gas
P₂ = new pressure of the gas (to be determined)
V₂ = new volume of the gas
T₂ = new temperature of the gas
Let's plug in the given values into the equation:
(P₁ × V₁) / (T₁) = (P₂ × V₂) / (T₂)
P₁ = 710. torr
V₁ = 5.0 × 102 mL
T₁ = 30.°C + 273.15 (converting to Kelvin)
V₂ = 27 mL
T₂ = 800.°C + 273.15 (converting to Kelvin)
Now, plug in the values and solve for P₂:
(710. torr × 5.0 × 102 mL) / (30.°C + 273.15) = (P₂ × 27 mL) / (800.°C + 273.15)
Simplifying the equation gives:
(710. torr × 5.0 × 102 mL) / (303.15 K) = (P₂ × 27 mL) / (1073.15 K)
Now, cross multiply and solve for P₂:
(710. torr × 5.0 × 102 mL × 1073.15 K) = (P₂ × 27 mL × 303.15 K)
Simplifying further:
(710 × 5.0 × 1073.15) = (P₂ × 27 × 303.15)
Multiplying and dividing:
3815777 = P₂ × 8207.05
Now, divide both sides by 8207.05 to solve for P₂:
P₂ = 3815777 / 8207.05
P₂ ≈ 465.46 torr
Therefore, the new pressure of the gas is approximately 465.46 torr.