A fixed quantity of gas at 27°C exhibits a pressure of 729 torr and occupies a volume of 5.70 L.
(a) Use Boyle's law to calculate the volume the gas will occupy if the pressure is increased to 1.75 atm while the temperature is held constant.
(b) Use Charles's law to calculate the volume the gas will occupy if the temperature is increased to 154°C while the pressure is held constant.
What is your question about this? The instructions seem to be very clear. Change temps to kelvins.
To solve these problems, we will use Boyle's law and Charles's law, which relate the volume, pressure, and temperature of a gas.
(a) Boyle's Law states that at a constant temperature, the pressure and volume of a gas are inversely proportional. The equation is: P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
In this case, the initial pressure is 729 torr, the initial volume is 5.70 L, and the final pressure is 1.75 atm. To find the final volume, we can rearrange the equation as follows: V2 = (P1 * V1) / P2.
Substituting the given values, we have:
V2 = (729 torr * 5.70 L) / (1.75 atm)
To make the units consistent, we need to convert the pressure from torr to atm. 1 atm = 760 torr, so 729 torr = 729/760 atm.
V2 = (729/760 atm * 5.70 L) / (1.75 atm)
V2 = 4.99 L
Therefore, the volume the gas will occupy if the pressure is increased to 1.75 atm while the temperature is held constant is approximately 4.99 L.
(b) Charles's law states that at a constant pressure, the volume and temperature of a gas are directly proportional. The equation is: V1 / T1 = V2 / T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
In this case, the initial temperature is 27°C, which we need to convert to Kelvin by adding 273.15 to it (27°C + 273.15 = 300.15 K). The initial volume is 5.70 L, and the final temperature is 154°C (154°C + 273.15 = 427.15 K).
To find the final volume, we can rearrange the equation as follows: V2 = (V1 * T2) / T1.
Substituting the given values, we have:
V2 = (5.70 L * 427.15 K) / 300.15 K
V2 = 8.12 L
Therefore, the volume the gas will occupy if the temperature is increased to 154°C while the pressure is held constant is approximately 8.12 L.