Question

What will be the new volume if the temperature remain constant ? The pressure on 2.50L of anaesthetic gas is change from 760mm Hg to 304mm Hg.​

Answer 1

`\boxed {\boxed {\sf 6.25 \ L}}`

Step-by-step explanation:

We are asked to find the new volume given a change in pressure. Since the temperature remains constant we are only concerned with volume and pressure. We will use Boyle's Law, which states the volume of a gas is inversely proportional to the pressure. The formula for this law is:

`P_1V_1= P_2V_2`

Initially, the volume of the gas is 2.50 liters and the pressure is 760 millimeters of mercury.

`760 \ mm \ Hg * 2.50 \ L = P_2V_2`

The pressure is changed to 304 millimeters of mercury, but the volume is unknown.

`760 \ mm \ Hg * 2.50 \ L = 304 \ mm \ Hg * V_2`

We are solving for the new volume so we must isolate the variable V₂. It is being multiplied by 304 millimeters of mercury. The inverse operation of multiplication is division. Divide both sides by 304 mm Hg.

`\frac {760 \ mm \ Hg * 2.50 \ L }{304 \ mm \ Hg}= (304 \ mm \ Hg * V_2)/(304 \ mm \ Hg)`

`\frac {760 \ mm \ Hg * 2.50 \ L }{304 \ mm \ Hg}= V_2`

The units of millimeters of mercury cancel out.

`\frac {760 * 2.50 \ L }{304 }= V_2`

`\frac {1900}{304} \ L =V_2`

`6.25 \ L =V_2`

The new volume of the anesthetic gas after the change in pressure is 6.25 liters.