Question

A gas sample occupies 10.28 L at 8.34 atm. Its volume at 6.98 atm (assuming constant temperature conditions) is Group of answer choices 12.28 L 8.60 L 15.61 L 5.66 L

Answer 1

`\boxed {\boxed {\sf 12.28 \ L}}}`

Step-by-step explanation:

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

`P_1V_1= P_2V_2`

Initially, the gas sample's volume is 10.28 liters at 8.34 atmospheres of pressure.

`8.34 \ atm * 10.28 \ L = P_2V_2`

Then, the pressure is lowered to 6.98 atmospheres, but the volume is unknown.

`8.34 \ atm * 10.28 \ L = 6.98 \ atm * V_2`

We are solving for the new volume, so we must isolate the variable V₂. It is being multiplied by 6.98 atmospheres. The inverse operation of multiplication is division, so we divide both sides by 6.98 atm.

`(8.34 \ atm * 10.28 \ L)/(6.98 \ atm) = (6.98 \ atm * V_2)/(6.98 \ atm)`

`(8.34 \ atm * 10.28 \ L)/(6.98 \ atm) =V_2`

The units of atmospheres cancel.

`(8.34 * 10.28 \ L)/(6.98 ) =V_2`

`\frac {85.7352}{6.98 } \ L =V_2`

`12.28297994 \ L = V_2`

Let's round to the nearest hundredth. The 2 in the thousandths place tells us to leave the 8 in the hundredth place.

`12.28 \ L \approx V_2`

The new volume at 6.98 atmospheres is approximately 12.28 liters.