Question

A gas of 190 mL at a pressure of 74 atm can be expected to change its pressure when its volume changes to 30.0 mL. Express its new pressure in units of atmospheres.

Answer 1

Answer : The new pressure of the gas will be, 468.66 atm

Explanation :

Boyle's Law : This law states that pressure of the gas is inversely proportional to the volume of the gas at constant temperature and number of moles.

$P\propto \frac{1}{V}$     (At constant temperature and number of moles)

or,

$P_1V_1=P_2V_2$

where,

$P_1$ = initial pressure of the gas = 74 atm

$P_2$ = final pressure of the gas = ?

$V_1$ = initial volume of the gas = 190 ml

$V_2$ = final volume of the gas = 30 ml

Now we put all the given values in the above formula, we get the final or new pressure of the gas.

$74atm\times 190ml=P_2\times 30ml$

$P_2=468.66atm$

Therefore, the new pressure of the gas will be, 468.66 atm

Answer 2

Answer: The new pressure of the gas is 467 atm.

Explanation:

To calculate the new pressure, we use the equation given by Boyle's law. This law states that pressure is inversely proportional to the volume of the gas at constant temperature.

The equation given by this law is:

$P_1V_1=P_2V_2$

where,

$P_1\text{ and }V_1$ are initial pressure and volume.

$P_2\text{ and }V_2$ are final pressure and volume.

We are given:

$P_1=74atm\\V_1=190mL\\P_2=?atm\\V_2=30.0mL$

Putting values in above equation, we get:

$74atm\times 190mL=P_2\times 30.0mL\\\\P_2=\frac{74\times 190}{30.0}=467atm$

Hence, the new pressure of the gas is 467 atm.