A container holds 500. mL of CO2 at 20. degrees C and 742 Torr. What will be the volume of the CO2 if the pressure is increased to 795 Torr?
Vf = .465 L
500 mL x (742/795) = 467 mL
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature is constant.
Boyle's Law equation: P1V1 = P2V2
Given:
Initial volume (V1) = 500 mL = 0.5 L (since 1 L = 1000 mL)
Initial pressure (P1) = 742 Torr
Final pressure (P2) = 795 Torr
Let's solve for the final volume (V2):
P1V1 = P2V2
(742 Torr)(0.5 L) = (795 Torr)(V2)
371 Torr * L = 795 Torr * V2
V2 = (371 Torr * L) / 795 Torr
V2 = 0.465 L
Therefore, the volume of the CO2 will be 0.465 L if the pressure is increased to 795 Torr.
To solve this problem, we will use the combined gas law equation, which relates the initial and final conditions of a gas sample. The combined gas law equation is as follows:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 and P2 are the initial and final pressures,
V1 and V2 are the initial and final volumes,
and T1 and T2 are the initial and final temperatures.
Let's assign the given values to the variables:
P1 = 742 Torr
V1 = 500 mL (which is 0.5 L since 1 L = 1000 mL)
T1 = 20 degrees C (which is 293 K)
P2 = 795 Torr
V2 = ? (To be determined)
The first step is to convert the temperatures from degrees Celsius to Kelvin. You can do that by adding 273.15 to the Celsius value. So, T1 = 293 K.
Next, we rearrange the equation to solve for the final volume V2:
V2 = (P2 * V1 * T1) / (P1 * T2)
Now we substitute the given values into the equation:
V2 = (795 Torr * 0.5 L * 293 K) / (742 Torr * T2)
We are now left with one unknown variable, T2. However, we can assume that the temperature remains constant because it is not mentioned in the problem that there is a change. Therefore, T2 is equal to T1, which is 293 K.
V2 = (795 Torr * 0.5 L * 293 K) / (742 Torr * 293 K)
Now we can cancel out the units and solve the equation:
V2 = (795 * 0.5) / (742)
V2 ≈ 0.536 L
Therefore, the volume of the CO2 will be approximately 0.536 L when the pressure is increased to 795 Torr.