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Chapter 12: Problem 36

A gas sample has a volume of 125 \(\mathrm{mL}\) at 91.0 \(\mathrm{kPa}\) . What will its volume be at 101 \(\mathrm{kPa}\) ?

Short Answer

Expert verified
Therefore, the volume of the gas at 101 \(\mathrm{kPa}\) will be approximately 113.3 \(\mathrm{mL}\)

Step by step solution

01

Understanding Boyle’s Law

Boyle’s Law states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. Mathematically, this can be stated as \( P_{1} V_{1} = P_{2} V_{2} \). Here \( P_{1} \) and \( V_{1} \) are the initial pressure and volume, and \( P_{2} \) and \( V_{2} \) are the final pressure and volume.
02

Insert the Known Values

Put the known values into the Boyle’s law equation, leaving the final volume \( V_{2} \) as the unknown variable to solve for. The equation becomes \( 91.0 kPa * 125 mL = 101 kPa * V_{2} \).
03

Solve for the Unknown Value

To solve for \( V_{2} \), divide both sides of the equation by 101 kPa. The equation then becomes \( V_{2} = (91.0 kPa * 125 mL) / 101 kPa \)
04

Perform the Calculation

Performing the calculation provides the final volume under the specified conditions. The calculation results in \( V_{2} \) approximately being 113.3 mL

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