Answer:
[tex]\boxed {\boxed {\sf 1058.3 \ L}}[/tex]
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:
[tex]\frac {V_1}{T_1}= \frac{V_2}{T_2}[/tex]
The gas was heated to 150 degrees Celsius and had a volume of 1587.4 liters.
[tex]\frac {1587.4 \ L }{150 \textdegree C} = \frac {V_2}{T_2}[/tex]
The temperature was 100 degrees Celsius, but the volume is unknown.
[tex]\frac {1587.4 \ L }{150 \textdegree C} = \frac {V_2}{100 \textdegree C}[/tex]
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.
[tex]100 \textdegree C *\frac {1587.4 \ L }{150 \textdegree C} = \frac {V_2}{100 \textdegree C} * 100 \textdegree C[/tex]
[tex]100 \textdegree C *\frac {1587.4 \ L }{150 \textdegree C} = V_2[/tex]
The units of degrees Celsius cancel.
[tex]100 *\frac {1587.4 \ L }{150 } = V_2[/tex]
[tex]100 *10.58266667 \ L = V_2[/tex]
[tex]1058.266667 \ L = V_2[/tex]
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.
[tex]1058.3 \ L = V_2[/tex]
The volume of the gas at 100 degrees Celsius is approximately 1058.3 liters.
