Question

According to Boyle's law, for a fixed quantity of gas at a given temperature, what quantity relating pressure P and volume V is constant? View Available Hint(s) According to Boyle's law, for a fixed quantity of gas at a given temperature, what quantity relating pressure and volume is constant?
a. PV
b. P×V
c. P+V
d. VP
Application of Boyle's law A 12-liter tank contains helium gas pressurized to 160 atm.
Part B What size tank would be needed to contain this same amount of helium at atmospheric pressure (1 atm)? Express the size in liters to three significant figures. View Available Hint(s) nothing LL

Answer 1

Answer: The quantity relating pressure and volume is $PV=k$ and the size of the tank must be $1.92\times 10^3L$

Explanation:

To calculate the new volume, 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.

Mathematically,

$P\propto \frac{1}{V}$

Or,

$PV=k$

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:

$P_1=160atm\\V_1=12L\\P_2=1atm\\V_2=?L$

Putting values in above equation, we get:

$160atm\times 12L=1atm\times V_2\\\\V_2=\frac{160\times 12}{1}=1920L=1.92\times 10^3L$

Hence, the size of the tank must be $1.92\times 10^3L$