Question

A gas that was heated to 150 Celsius has a new volume of 1587.4 L. What was its volume when its temperature was 100 Celsius?

Answer 1

`\boxed {\boxed {\sf 1058.3 \ L}}`

Step-by-step explanation:

We are asked to find the new volume of a gas after a change in temperature. We will use Charles's Law, which states the volume of a gas is directly proportional to the temperature. The formula for this law is:

`\frac {V_1}{T_1}= (V_2)/(T_2)`

The gas was heated to 150 degrees Celsius and had a volume of 1587.4 liters.

`\frac {1587.4 \ L }{150 \textdegree C} = \frac {V_2}{T_2}`

The temperature was 100 degrees Celsius, but the volume is unknown.

`\frac {1587.4 \ L }{150 \textdegree C} = \frac {V_2}{100 \textdegree C}`

We are solving for the volume at 100 degrees Celsius, so we must isolate the variable V₂. It is being divided by 100°C and the inverse of division is multiplication. Multiply both sides of the equation by 100°C.

`100 \textdegree C *\frac {1587.4 \ L }{150 \textdegree C} = \frac {V_2}{100 \textdegree C} * 100 \textdegree C`

`100 \textdegree C *\frac {1587.4 \ L }{150 \textdegree C} = V_2`

The units of degrees Celsius cancel.

`100 *\frac {1587.4 \ L }{150 } = V_2`

`100 *10.58266667 \ L = V_2`

`1058.266667 \ L = V_2`

The original measurement of volume has 5 significant figures, so our answer must have the same. For the number we calculated, that is the tenth place. The 6 in the hundredth place to the right tells us to round to 2 up to a 3.

`1058.3 \ L = V_2`

The volume of the gas at 100 degrees Celsius is approximately 1058.3 liters.