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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 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.
[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.