To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas. The formula is given as:
P1V1 / T1 = P2V2 / T2
Where: P1 = Initial pressure V1 = Initial volume T1 = Initial temperature P2 = Final pressure (what we're trying to find) V2 = Final volume T2 = Final temperature (assuming it remains constant)
Given: P1 = 800 mmHg V1 = 10.00 liters P2 = 700 mmHg
Let's assume the temperature remains constant, so T1 = T2. Now we can plug in the values and solve for V2:
P1V1 / T1 = P2V2 / T2
(800 mmHg)(10.00 L) / T1 = (700 mmHg)(V2) / T1
Canceling out the T1 on both sides of the equation:
(800 mmHg)(10.00 L) = (700 mmHg)(V2)
Dividing both sides of the equation by 700 mmHg:
(800 mmHg)(10.00 L) / 700 mmHg = V2
80.00 L = V2
Therefore, the volume of the gas that exerts a pressure of 700 mmHg, assuming the temperature remains constant, is 80.00 liters.