Answer:
[tex]\boxed {\boxed {\sf 12.28 \ L}}}[/tex]
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:
[tex]P_1V_1= P_2V_2[/tex]
Initially, the gas sample's volume is 10.28 liters at 8.34 atmospheres of pressure.
[tex]8.34 \ atm * 10.28 \ L = P_2V_2[/tex]
Then, the pressure is lowered to 6.98 atmospheres, but the volume is unknown.
[tex]8.34 \ atm * 10.28 \ L = 6.98 \ atm * V_2[/tex]
We are solving for the new volume, so we must isolate the variable Vā. It is being multiplied by 6.98 atmospheres. The inverse operation of multiplication is division, so we divide both sides by 6.98 atm.
[tex]\frac{8.34 \ atm * 10.28 \ L}{6.98 \ atm} = \frac{6.98 \ atm * V_2}{6.98 \ atm}[/tex]
[tex]\frac{8.34 \ atm * 10.28 \ L}{6.98 \ atm} =V_2[/tex]
The units of atmospheres cancel.
[tex]\frac{8.34 * 10.28 \ L}{6.98 } =V_2[/tex]
[tex]\frac {85.7352}{6.98 } \ L =V_2[/tex]
[tex]12.28297994 \ L = V_2[/tex]
Let's round to the nearest hundredth. The 2 in the thousandths place tells us to leave the 8 in the hundredth place.
[tex]12.28 \ L \approx V_2[/tex]
The new volume at 6.98 atmospheres is approximately 12.28 liters.
