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.

a) P1V1 = P2V2

b) V1/T1 = V1/T2

im not sure how to plug the numbers in correctly

Plug the pressures into the P slots and the volumes into the V spots.

Oh and leave a variable for the number you want. Solve.

To solve these problems, we can use the ideal gas laws, which include Boyle's law and Charles's law. Boyle's law states that the pressure and volume of a gas are inversely proportional when the temperature is constant, while Charles's law states that the volume and temperature of a gas are directly proportional when the pressure is constant. Let's solve the problems step by step.

(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.

Step 1: Write down the given information:
Initial pressure (P1) = 729 torr
Initial volume (V1) = 5.70 L
Final pressure (P2) = 1.75 atm

Step 2: Convert the initial pressure to the same units as the final pressure (atm):
To convert torr to atm, divide by 760.
P1 = 729 torr / 760 torr/atm = 0.96 atm

Step 3: Apply Boyle's law to find the final volume:
Boyle's Law states: P1 * V1 = P2 * V2
0.96 atm * 5.70 L = 1.75 atm * V2

Step 4: Solve for V2:
V2 = (0.96 atm * 5.70 L) / 1.75 atm
V2 = 3.13 L

Therefore, the gas will occupy a volume of 3.13 L 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.

Step 1: Write down the given information:
Initial temperature (T1) = 27°C
Initial volume (V1) = 5.70 L
Final temperature (T2) = 154°C

Step 2: Convert the temperatures to Kelvin:
To convert from Celsius to Kelvin, add 273.15.
T1 = 27°C + 273.15 = 300.15 K
T2 = 154°C + 273.15 = 427.15 K

Step 3: Apply Charles's law to find the final volume:
Charles's Law states: V1 / T1 = V2 / T2
5.70 L / 300.15 K = V2 / 427.15 K

Step 4: Solve for V2:
V2 = (5.70 L * 427.15 K) / 300.15 K
V2 = 8.10 L

Therefore, the gas will occupy a volume of 8.10 L if the temperature is increased to 154°C while the pressure is held constant.