At 10 degree Celsius a sample of carbon dioxide gas has a volume of 25.5 mL under pressure of 758 mmHg. What would the volume of the CO2 sample be at STP?
(P1V1/T1) = (P2V2/T2)
To find the volume of the CO2 sample at STP (Standard Temperature and Pressure), we need to know the conditions of STP.
STP is defined as a temperature of 0 degrees Celsius (273.15 Kelvin) and a pressure of 1 atmosphere (760 mmHg or 101.3 kPa).
Since we know the initial conditions of the sample (10 degrees Celsius and 758 mmHg), we can use the combined gas law equation to solve for the volume at STP.
The combined gas law equation is given as follows:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ and P₂ are the initial and final pressures
V₁ and V₂ are the initial and final volumes
T₁ and T₂ are the initial and final temperatures
Let's substitute the values into the equation and solve for V₂ (the final volume at STP).
P₁ = 758 mmHg
V₁ = 25.5 mL
T₁ = 10 degrees Celsius (or 10 + 273.15 = 283.15 Kelvin)
P₂ = 1 atmosphere (or 760 mmHg)
T₂ = 0 degrees Celsius (or 0 + 273.15 = 273.15 Kelvin)
Now we can plug in the values into the equation:
(758 mmHg * 25.5 mL) / (283.15 K) = (760 mmHg * V₂) / (273.15 K)
Simplifying the equation, we get:
(758 * 25.5) / 283.15 = (760 * V₂) / 273.15
Solving for V₂:
(758 * 25.5) * 273.15 = 760 * V₂ * 283.15
1943920.03 = 2157714.8 * V₂
V₂ = 1943920.03 / 2157714.8
V₂ ≈ 0.901 mL (rounded to three decimal places)
Therefore, the volume of the CO2 sample at STP would be approximately 0.901 mL.