we have 159ml of CO2 at 38.9 C and 92.4 kPa. if the conditions change to 64.9 C and 174 kPa, what is the volume of the gas?
To compute the volume of the gas with the given conditions, we need to use the combined gas law equation. The combined gas law relates the initial and final conditions of a gas sample:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
where:
P₁ and P₂ are the initial and final pressures, respectively, in units of pressure (kPa),
V₁ and V₂ are the initial and final volumes, respectively, in units of volume (ml or cm³),
T₁ and T₂ are the initial and final temperatures, respectively, in units of temperature (Kelvin).
In this case, we are given:
P₁ = 92.4 kPa
V₁ = 159 ml
T₁ = 38.9°C (which must be converted to Kelvin, as the equation requires it)
And we need to find:
V₂ (the final volume)
First, let's convert the initial temperature from Celsius to Kelvin:
T₁ (in Kelvin) = T₁ (in Celsius) + 273.15
T₁ (in Kelvin) = 38.9 + 273.15 = 312.05 K
Now we can substitute these values into the combined gas law equation and solve for V₂:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
Simplifying, we get:
V₂ = (P₂ * V₁ * T₂) / (P₁ * T₁)
Now let's substitute the given values:
P₁ = 92.4 kPa
V₁ = 159 ml
T₁ = 312.05 K
P₂ = 174 kPa
T₂ = 64.9°C (which must also be converted to Kelvin)
Converting:
T₂ (in Kelvin) = T₂ (in Celsius) + 273.15
T₂ (in Kelvin) = 64.9 + 273.15 = 338.05 K
Now we can calculate V₂:
V₂ = (174 * 159 * 338.05) / (92.4 * 312.05)
Calculating this expression will give us the final volume of the gas.