A sample of gas has a volume of 50 mL and an initial temperature of 380 K. The temperature must be changed to _____ K in order to halve the volume. Assume constant pressure and amount for the gas.
(v1/T1) = (v2/T2)
Don't forget to use T in kelvin.
i have know idea how to even figure it out with just volume 1 and temp 1. i have tried multiple ways with the equation but not getting anywhere
To halve the volume of the gas, we can use the combined gas law equation:
(V1/T1) = (V2/T2)
Where:
V1 = initial volume = 50 mL
T1 = initial temperature = 380 K
V2 = final volume (halved volume)
T2 = final temperature (unknown)
To solve for T2, we rearrange the equation as:
T2 = (V2 * T1) / V1
Since we want to halve the initial volume, V2 will be 50 mL / 2 = 25 mL.
Plugging in these values into the equation, we get:
T2 = (25 mL * 380 K) / 50 mL
T2 = (25 * 380) / 50
T2 = 1900 / 50
T2 = 38 K
Therefore, the temperature must be changed to 38 K in order to halve the volume of the gas.
To find the final temperature required to halve the volume of the gas, we can use the combined gas law:
P₁V₁/T₁ = P₂V₂/T₂
In this case, the initial volume (V₁) is 50 mL, and the initial temperature (T₁) is 380 K. We want to find the final temperature (T₂) when the volume is halved (V₂ = V₁/2).
Since we are assuming constant pressure and amount for the gas, the pressure (P₁) and pressure (P₂) will remain the same and can be canceled out from the equation.
The equation becomes:
V₁/T₁ = V₂/T₂
Plugging in the values, we have:
50 mL / 380 K = (50 mL/2) / T₂
Simplifying further, we get:
T₂ = T₁ * (V₂ / V₁)
T₂ = 380 K * (50 mL/2) / 50 mL
Now, we can calculate the final temperature:
T₂ = 190 K
Therefore, the temperature must be changed to 190 K in order to halve the volume.