A fixed quantity of gas at 22°C exhibits a pressure of 739 torr and occupies a volume of 5.46

P1V1=P2V2

To calculate the volume of the gas at a new pressure while the temperature is held constant, we can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional when the temperature is constant.

The equation for Boyle's Law is:

P1 * V1 = P2 * V2

Where:

P1 = initial pressure
V1 = initial volume
P2 = new pressure
V2 = new volume

In this case:
P1 = 739 torr
V1 = 5.46 L
P2 = 1.74 atm

First, we need to convert the initial pressure from torr to atm:
1 atm = 760 torr

So, P1 = 739 torr / 760 torr/atm = 0.971 atm

Now we can substitute the values into the Boyle's Law equation:

0.971 atm * 5.46 L = 1.74 atm * V2

Solving for V2, we get:

V2 = (0.971 atm * 5.46 L) / 1.74 atm

V2 = 3.06 L

Therefore, the volume of the gas will occupy approximately 3.06 L if the pressure is increased to 1.74 atm while the temperature is held constant.