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Chapter 1: Problem 40

A certain mass of a gas occupies a volume of 600 \(\mathrm{ml}\) at a certain temperature and pressure. If pressure is decreased by \(40 \%\) what will be the volume occupied by the same mass of the gas at the same temperature? (a) \(240 \mathrm{ml}\) (b) \(1000 \mathrm{ml}\) (c) \(300 \mathrm{ml}\) (d) \(120 \mathrm{ml}\)

Short Answer

Expert verified
(a) 800 ml (b) 1000 ml (c) 1200 ml (d) 1500 ml Answer: (b) 1000 ml

Step by step solution

01

Understanding Boyle's Law

Boyle's law states that for a given mass of a gas at constant temperature, the pressure multiplied by the volume (P x V) remains the same. Mathematically, it is represented as: \({P_1}{V_1} = {P_2}{V_2}\), where \(P_1\) and \(V_1\) are the initial pressure and volume, and \(P_2\) and \(V_2\) are the final pressure and volume.
02

Convert the given information

We are given that the initial volume is \(600ml\), and the pressure decreases by \(40 \%\). We can represent these as \(V_1 = 600ml\), and \(P_2 = 0.6P_1\) \((P_2=100\%-40\%=60\% \times P_1)\). We will use these values to find the final volume (\(V_2\)) occupied by the gas.
03

Apply Boyle's Law

Using the values from Step 2, we can substitute them into the equation for Boyle's law: \({P_1}{V_1} = {P_2}{V_2}\). Therefore, \({P_1}{600} = (0.6{P_1}){V_2}\). Notice that we can cancel out \({P_1}\) from both sides of the equation, since it is not zero, to leave us with \(600 = 0.6{V_2}\).
04

Solve for the final volume (\(V_2\))

Now, we simply need to solve for the final volume (\(V_2\)) by dividing both sides of the equation by \(0.6\): \({V_2} = \frac{600}{0.6}= 1000 \thinspace \mathrm{ml}\).
05

Identify the answer

We found that the final volume (\(V_2\)) is \(1000 \thinspace \mathrm{ml}\). Therefore, the correct answer is (b) \(1000 \thinspace \mathrm{ml}\).

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