change temps to Kelvins.
combined gas law:
p1V1T2=P2V2T1
combined gas law:
p1V1T2=P2V2T1
The formula for the combined gas law is:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ = initial pressure
V₁ = initial volume
T₁ = initial temperature
P₂ = final pressure
V₂ = final volume
T₂ = final temperature
Now, let's plug in the given values into the formula:
P₁ = 760 mmHg
V₁ = 20 cm³
T₁ = 5°C + 273.15 = 278.15 K
P₂ = 800 mmHg
T₂ = 30°C + 273.15 = 303.15 K
Plug in the values into the formula:
(760 mmHg * 20 cm³) / (278.15 K) = (800 mmHg * V₂) / (303.15 K)
Now, rearrange the formula to solve for V₂ (final volume):
V₂ = [(760 mmHg * 20 cm³ * 303.15 K) / (278.15 K * 800 mmHg)]
Now, solve the equation:
V₂ = (18,450 mmHg * cm³ * K) / (222,520 mmHg)
Calculating:
V₂ ≈ 0.0829 cm³
Therefore, the volume of the gas at 30°C and 800 mmHg pressure is approximately 0.0829 cm³.