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Chapter 6: Problem 12

We want to change the volume of a fixed amount of gas from \(725 \mathrm{mL}\) to 2.25 L while holding the temperature constant. To what value must we change the pressure if the initial pressure is \(105 \mathrm{kPa} ?\)

Short Answer

Expert verified
The pressure needs to be changed to approximately \(33.375 \mathrm{kPa}\).

Step by step solution

01

Make sure the units of volume are consistent

Before applying Boyle's law, check the units of volume. Here, the initial volume is given in milliliter (mL) and the final volume in liter (L). As 1 L = 1000 mL, convert 2.25 L to 2250 mL for consistency.
02

Apply Boyle's Law

Using \( P_1V_1=P_2V_2 \), where \( P_1 = 105 \mathrm{kPa} \), \( V_1 = 725 \mathrm{mL} \), and \( V_2 = 2250 \mathrm{mL} \), you can solve for \( P_2 \), the final pressure.
03

Solve Algebraically

Rearrange the Boyle's Law equation to isolate \( P_2 \): \( P_2 = P_1V_1/V_2 \). Substituting the known values gives \( P_2 = 105 \mathrm{kPa} \times 725 \mathrm{mL} / 2250 \mathrm{mL} \)
04

Solve Numerically

Performing the calculation gives \( P_2 \approx 33.375 \mathrm{kPa} \).

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Most popular questions from this chapter

The gas with the greatest density at STP is (a) \(\mathrm{N}_{2} \mathrm{O}\) (b) \(\mathrm{Kr} ;\) (c) \(\mathrm{SO}_{3} ;\) (d) \(\mathrm{Cl}_{2}\).

A nitrogen molecule ( \(\mathrm{N}_{2}\) ) having the average kinetic energy at \(300 \mathrm{K}\) is released from Earth's surface to travel upward. If the molecule could move upward without colliding with other molecules, then how high would it go before coming to rest? Give your answer in kilometers. [Hint: When the molecule comes to rest, the potential energy of the molecule will be \(m g h\) where \(m\) is the molecular mass in kilograms, \(g=9.81 \mathrm{m} \mathrm{s}^{-2}\) is the acceleration due to gravity, and \(h\) is the height, in meters, above Earth's surface.]

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