A sample of carbon dioxide gas occupies 566 mL at 0.825 atm and 15 ◦C. What will the pressure be at a volume of 834 mL and a temperature of 20◦C
since PV/T = k is constant,
(.825)(566)/(273+15) = P(834)/(273+20)
To solve this problem, we will use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature of a gas sample. The combined gas law is given by:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
where:
P₁ and P₂ are the initial and final pressures of the gas,
V₁ and V₂ are the initial and final volumes of the gas,
T₁ and T₂ are the initial and final temperatures of the gas.
We are given:
P₁ = 0.825 atm (initial pressure)
V₁ = 566 mL (initial volume)
T₁ = 15°C + 273.15 = 288.15 K (initial temperature)
We need to find P₂ (final pressure) when:
V₂ = 834 mL (final volume)
T₂ = 20°C + 273.15 = 293.15 K (final temperature)
Using the combined gas law equation, we can rearrange it to solve for P₂:
P₂ = (P₁ * V₁ * T₂) / (V₂ * T₁)
Plugging in the given values:
P₂ = (0.825 atm * 566 mL * 293.15 K) / (834 mL * 288.15 K)
Note: Make sure to convert all volumes to liters and temperatures to Kelvin.
First, let's convert mL to L:
V₁ = 566 mL = 0.566 L
V₂ = 834 mL = 0.834 L
Next, we calculate:
P₂ = (0.825 atm * 0.566 L * 293.15 K) / (0.834 L * 288.15 K)
P₂ ≈ 0.915 atm
Therefore, the pressure at a volume of 834 mL and a temperature of 20°C would be approximately 0.915 atm.