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Chapter 9: Problem 1247

When the pressure on \(1200 \mathrm{ml}\) of a gas is increased from $70 \mathrm{~cm}\( to \)120 \mathrm{~cm}$ of mercury at constant temperature, the new volume of the gas will be (A) \(400 \mathrm{ml}\) (B) \(600 \mathrm{ml}\) (C) \(700 \mathrm{ml}\) (D) \(500 \mathrm{ml}\)

Short Answer

Expert verified
Using Boyle's Law, \(P_1V_1 = P_2V_2\), where \(P_1 = 70 \: \mathrm{cm\: Hg}\), \(P_2 = 120 \: \mathrm{cm\: Hg}\), and \(V_1 = 1200 \: \mathrm{ml}\). Solve for the new volume, \(V_2\): \(V_2 = \frac{P_1V_1}{P_2} = \frac{70 \times 1200}{120} = 700 \: \mathrm{ml}\). The correct answer is (C) \(700 \mathrm{~ml}\).

Step by step solution

01

Remember Boyle's Law formula

Boyle's Law states that for a constant temperature and mass of gas, the pressure multiplied by the volume is constant. mathematically, Boyle's law is expressed as: \(P_1V_1 = P_2V_2\) 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 given pressure values to the same unit

The given pressure values are in cm of mercury. To make the calculations, we need to convert them to the same units (for example, Pascals or atm). However, in this problem, we don't need to worry about the units, because the pressure is given in the same unit (cm of mercury), and it will cancel out in the calculation.
03

Substitute the values into the formula

Let's first write down the initial and final pressure values, as well as the initial volume of the gas: \(P_1 = 70 \: \mathrm{cm\: Hg}\) \(P_2 = 120 \: \mathrm{cm\: Hg}\) \(V_1 = 1200 \: \mathrm{ml}\) Now, use the Boyle's Law formula: \(P_1V_1 = P_2V_2\) \(70 \: \mathrm{cm\: Hg} \times 1200 \: \mathrm{ml} = 120 \: \mathrm{cm\: Hg} \times V_2\)
04

Solve for the new volume (V2)

We need to find the new volume (V2), so we can now isolate V2 and solve for it: \(V_2 = \frac{P_1V_1}{P_2}\) Now, plug in the given values: \(V_2 = \frac{70 \: \mathrm{cm\: Hg} \times 1200 \: \mathrm{ml}}{120 \: \mathrm{cm\: Hg}}\)
05

Calculate the new volume and check the answer

Perform the arithmetic to find the new volume: \(V_2 = \frac{(70 \times 1200)}{120}\) \(V_2 = \frac{84000}{120}\) \(V_2 = 700 \: \mathrm{ml}\) So, the new volume of the gas is \(700 \: \mathrm{ml}\). Therefore, the correct answer is (C) \(700 \mathrm{~ml}\).

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