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CHEMISTRY, M2 EQ-Bank 7v3

Consider a sample of gas confined in a cylinder equipped with a movable piston. The initial pressure of the gas is 1.2 atmospheres, and the initial volume is 6.0 litres. The piston is then adjusted to change the volume of the gas.

Assuming the temperature of the gas remains constant throughout the process, calculate the new pressure of the gas when the volume is adjusted to:

  1. 3.0 litres  (2 marks)
  2. 12.0 litres  (2 marks)
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a.    \(2.4\ \text{atm}\)

b.    \(0.6\ \text{atm}\)

Show Worked Solution

Boyle’s Law is mathematically expressed as \( P_1V_1 = P_2V_2 \).

a.    \( P_1 = 1.2 \, \text{atm} \)

\( V_1 = 6.0 \, \text{L} \)

\( V_2 = 3.0 \, \text{L} \)

\( P_2 = \dfrac{P_1 \times V_1}{V_2} = \dfrac{1.2 \, \text{atm} \times 6.0 \, \text{L}}{3.0 \, \text{L}} = 2.4 \, \text{atm}\)
 

b.    \( V_2 = 12.0 \, \text{L} \)

\( P_2 = \dfrac{P_1 \times V_1}{V_2} = \dfrac{1.2 \, \text{atm} \times 6.0 \, \text{L}}{12.0 \, \text{L}} = 0.6 \, \text{atm}\)

CHEMISTRY, M2 EQ-Bank 7v4

Consider a sample of gas confined in a cylinder equipped with a movable piston. The initial pressure of the gas is 2.5 atmospheres, and the initial volume is 2.0 litres. The piston is then adjusted to change the volume of the gas.

Assuming the temperature of the gas remains constant throughout the process, calculate the new pressure of the gas when the volume is adjusted to:

  1. 1.0 litre  (2 marks)
  2. 4.0 litres  (2 marks)
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a.    \(5.0\ \text{atm}\)

b.    \(1.25\ \text{atm}\)

Show Worked Solution

a.   Boyle’s Law is mathematically expressed as \( P_1V_1 = P_2V_2 \).

\( P_1 = 2.5 \, \text{atm} \)

\( V_1 = 2.0 \, \text{L} \)

\( V_2 = 1.0 \, \text{L} \)

\( P_2 = \dfrac{P_1 \times V_1}{V_2} = \dfrac{2.5 \, \text{atm} \times 2.0 \, \text{L}}{1.0 \, \text{L}} = 5.0 \, \text{atm}\)
 

b.    \( V_2 = 4.0 \, \text{L} \)

\( P_2 = \dfrac{P_1 \times V_1}{V_2} = \dfrac{2.5 \, \text{atm} \times 2.0 \, \text{L}}{4.0 \, \text{L}} = 1.25 \, \text{atm}\)

CHEMISTRY, M2 EQ-Bank 7v3

Consider a sample of gas confined in a cylinder equipped with a movable piston. The initial pressure of the gas is 1.8 atmospheres, and the initial volume is 5.0 litres. The piston is then adjusted to change the volume of the gas.

Calculate the new pressure of the gas when the volume is adjusted to:

  1. 2.5 litres  (2 marks)
  2. 10.0 litres  (2 marks)

Assume the temperature of the gas remains constant throughout the process.

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a.    \(3.6\ \text{atm}\)

b.    \(0.9\ \text{atm}\)

Show Worked Solution

a.   Boyle’s Law is mathematically expressed as \( P_1V_1 = P_2V_2 \).

\( P_1 = 1.8 \, \text{atm} \)

\( V_1 = 5.0 \, \text{L} \)

\( V_2 = 2.5 \, \text{L} \)

\( P_2 = \dfrac{P_1 \times V_1}{V_2} = \dfrac{1.8 \, \text{atm} \times 5.0 \, \text{L}}{2.5 \, \text{L}} = 3.6 \, \text{atm}\)
 

b.    \( V_2 = 10.0 \, \text{L} \)

\( P_2 = \dfrac{P_1 \times V_1}{V_2} = \dfrac{1.8 \, \text{atm} \times 5.0 \, \text{L}}{10.0 \, \text{L}} = 0.9 \, \text{atm}\)

CHEMISTRY, M2 EQ-Bank 5

Consider a sample of gas confined in a cylinder equipped with a movable piston. The initial pressure of the gas is 2.0 atmospheres, and the initial volume is 3.0 litres. The piston is then adjusted to change the volume of the gas.

Assuming the temperature of the gas remains constant throughout the process, calculate the new pressure of the gas when the volume is adjusted to:

  1. 1.5 litres   (2 marks)
  2. 6.0 litres   (2 marks)
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a.    \(4.0\ \text{atm}\)

b.    \(1.0\ \text{atm}\)

Show Worked Solution

a.   Boyle’s Law is mathematically expressed as \( P_1V_1 = P_2V_2 \).

\( P_1 = 2.0 \, \text{atm} \)

\( V_1 = 3.0 \, \text{L} \)

\( V_2 = 1.5 \, \text{L} \)

\( P_2 = \dfrac{P_1 \times V_1}{V_2} = \dfrac{2.0 \, \text{atm} \times 3.0 \, \text{L}}{1.5 \, \text{L}} = 4.0 \, \text{atm}\)
 

b.    \( V_2 = 6.0 \, \text{L} \)

\( P_2 = \dfrac{P_1 \times V_1}{V_2} = \dfrac{2.0 \, \text{atm} \times 3.0 \, \text{L}}{6.0 \, \text{L}} = 1.0 \, \text{atm}\)

CHEMISTRY, M2 EQ-Bank 2

During a laboratory experiment, a gas is collected in a sealed syringe. Initially, the gas has a volume of 5.0 litres and a pressure of 1.0 atmosphere. 

  1.  Calculate the new pressure inside the syringe when the volume is decreased to 3.0 litres, assuming no temperature change.   (2 marks)

  2. After reaching the pressure calculated in part a, the volume is further decreased so that the pressure inside the syringe doubles. Calculate the final volume of the gas.   (2 marks)

  3. Discuss two potential experimental errors that could affect the accuracy of the observed results compared to the theoretical predictions of Boyle's Law.   (2 marks)

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a.    \(1.67\ \text{atm}\)

b.    \(1.5\ \text{L}\)

c.    Potential experimental errors could include:

→ Temperature Control. Any temperature changes violate the assumptions of Boyle’s Law which holds only at constant temperature.

→ Measurement Accuracy. Errors in measuring volume changes can lead to inaccuracies in pressure calculations.

→ Non-Ideal Behaviour. At high pressures, gases may deviate from ideal behaviour, affecting the accuracy of Boyle’s Law predictions.

Show Worked Solution

a.    Using Boyle’s Law  \( P_1V_1 = P_2V_2 \):

\( P_1 = 1.0 \, \text{atm}, \quad V_1 = 5.0 \, \text{L}, \quad V_2 = 3.0 \, \text{L} \)

\(P_2 = \dfrac{P_1 \times V_1}{V_2} = \dfrac{1.0 \times 5.0}{3.0} = 1.67 \, \text{atm} \)
 

b.    To find the new volume when pressure doubles:

\( P_3 = 2 \times P_2 = 2 \times 1.67 \, \text{atm} = 3.34 \, \text{atm}\)

\( P_1V_1 = P_3V_3 \ \  \Rightarrow \ \  V_3 = \dfrac{P_1 \times V_1}{P_3} = \dfrac{1.0  \times 5.0 }{3.34} \approx 1.5 \, \text{L}\)
 

c.    Potential experimental errors could include:

→ Temperature Control. Any temperature changes violate the assumptions of Boyle’s Law which holds only at constant temperature.

→ Measurement Accuracy. Errors in measuring volume changes can lead to inaccuracies in pressure calculations.

→ Non-Ideal Behaviour. At high pressures, gases may deviate from ideal behaviour, affecting the accuracy of Boyle’s Law predictions.

CHEMISTRY, M2 EQ-Bank 1

A cylinder equipped with a movable piston contains an inert gas. The initial pressure of the gas is 1.5 atmospheres, and the cylinder's initial volume is 4.0 litres.

The piston is then adjusted to change the volume of the cylinder.

Assuming the temperature of the gas remains constant throughout the process, calculate the new pressure of the gas when the volume is adjusted to 2.0 litres.   (2 marks)

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\(3.0\ \text{atm}\)

Show Worked Solution

\(P_1 = 1.5\ \text{atm},\ \ V_1 = 4.0\ \text{L},\ \ V_2 = 2.0\ \text{L} \)

Boyle’s Law  \(\Rightarrow \ P_1V_1 = P_2V_2 \).

\( P_2 = \dfrac{P_1 \times V_1}{V_2} = \dfrac{1.5 \, \text{atm} \times 4.0 \, \text{L}}{2.0 \, \text{L}} = 3.0 \, \text{atm}\)

CHEMISTRY, M2 EQ-Bank 4

A cylinder equipped with a movable piston contains an inert gas. The initial pressure of the gas is 1.35 atmospheres, and the cylinder's initial volume is 5.0 litres.

The piston is then adjusted to change the volume of the cylinder.

Assuming the temperature of the gas remains constant throughout the process, calculate the new pressure of the gas when the volume of the cylinder is adjusted to 8.0 litres.   (2 marks)

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\(0.84\ \text{atm}\)

Show Worked Solution

\(V_1 = 5.0\ \text{L},\ \ V_2 = 8.0\ \text{L},\ \ P_1=1.35\ \text{atm} \)

Boyle’s Law  \(\Rightarrow \ P_1V_1 = P_2V_2 \).

\(P_2 = \dfrac{P_1 \times V_1}{V_{2}} = \dfrac{1.35\ \text{atm} \times 5.0\ \text{L}}{8.0\ \text{L}} = 0.84\ \text{atm}\)