The VoLume of a gas is 15.0 L when the temperature is 75.0°C. If the temperature is changed to standard temperature without changing the pressure, what is the new volume?
When pressure is constant:
P1/T1 = P2/T2
Temperature should be in °K.
18.024l
To find the new volume when the temperature is changed to standard temperature (0°C or 273.15K), we can use the combined gas law. The combined gas law relates the initial and final volumes and temperatures of a gas sample, assuming the pressure remains constant.
The combined gas law equation is as follows:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Where:
P₁ = Initial pressure
V₁ = Initial volume
T₁ = Initial temperature
P₂ = Final pressure (remains constant)
V₂ = Final volume (to be determined)
T₂ = Final temperature (standard temperature = 0°C or 273.15K)
In this case, we are told that the initial volume (V₁) is 15.0 L and the initial temperature (T₁) is 75.0°C. We need to find the final volume (V₂) when the temperature is changed to standard temperature.
Let's substitute the given values into the equation:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
Since the pressure is given as constant, we can simplify the equation to:
V₁ / T₁ = V₂ / T₂
Now, let's plug in the values:
15.0 L / 75.0°C = V₂ / 0°C (or 273.15K)
To convert Celsius to kelvin, we add 273.15:
15.0 L / (75.0 + 273.15)K = V₂ / 273.15K
Calculating the right side of the equation:
V₂ / 273.15 = 15.0 L / (75.0 + 273.15)
Simplifying the right side of the equation:
V₂ / 273.15 = 15.0 L / 348.15
Now, cross-multiply and solve for V₂:
V₂ = (15.0 L / 348.15) * 273.15
V₂ ≈ 11.8 L
Therefore, when the temperature is changed to standard temperature without changing the pressure, the new volume is approximately 11.8 L.