Question

A sample of an ideal gas occupies 2.78 x 10^3 mL at 25°C and 760 mm Hg.

Answer 1

Answer: It will occupy $4.45\times 10^3ml$ at the same temperature and 475 mm Hg.

Explanation:

Boyle's Law: This law states that pressure 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)

$P_1V_1=P_2V_2$    (At constant temperature and number of moles)

where,

$P_1$ = initial pressure of gas = 760 mm Hg

$P_2$ = final pressure of gas = 475 mm Hg

$V_1$ = initial volume of gas = $2.78\times 10^3ml$

$V_2$  = final volume of gas = ?

Putting in the values:

$760mm Hg\times 2.78\times 10^3ml=475 mm Hg\times V_2$

$V_2=4.45\times 10^3ml$

Thus it will occupy $4.45\times 10^3ml$ at the same temperature and 475 mm Hg

Answer 2

Answer:

The volume at 475 mmHg is 4.448 L

Explanation:

Step 1: Data given

Volume = 2.78 * 10³ mL = 2.78 L

Temperature = 25.0 °C

Pressure = 760 mmHg = 1 atm

The temperature stays the same

The pressure lowers to 475 mmHg = 475/760 = 0.625 atm

Step 2: Calculate the new volume

P1V1 = P2V2

⇒ with P1 = the initial pressure = 1 atm

⇒ with V1 = the initial volume = 2.78 L

⇒ with P2 = the final pressure = 0.625 atm

⇒ with V2 = the final volume = TO BE DETERMINED

V2 = 4.448 L

The volume at 475 mmHg is 4.448 L