Answer:
[tex]\boxed {\boxed {\sf 225 \ mL}}[/tex]
Explanation:
The temperature and volume of the gas are changing, so we use Charles's Law. This states the temperature of a gas is directly proportional to the volume of a gas. The formula is:
[tex]\frac{V_1}{T_1}=\frac{V_2}{T_2}[/tex]
The original volume is unknown. The new volume is 75 milliliters.
The gas is cooled from 150 Kelvin to 50 Kelvin, so the original temperature is 150 K and the new temperature is 50 K.
We know that:
- T₁= 150 K
- V₂= 75 mL
- T₂= 50 K
Substitute the values into the formula.
[tex]\frac {V_1}{150 \ K}=\frac{ 75 \ mL}{50 \ K}[/tex]
Since we are solving for the original volume, we must isolate the variable V₁.
It is being divided by 150 K. The inverse of division is multiplication, so we multiply both sides by 150 K.
[tex]150 \ K *\frac {V_1}{150 \ K}=\frac{ 75 \ mL}{50 \ K}* 150 \ K[/tex]
[tex]V_1=\frac{ 75 \ mL}{50 \ K}* 150 \ K[/tex]
The units of Kelvin (K) cancel.
[tex]V_1= \frac{ 75 \ mL}{50 }* 150[/tex]
[tex]V_1=1.5 * 150 \ mL[/tex]
[tex]V_1= 225 \ mL[/tex]
The original volume is 225 milliliters.
