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CHEMISTRY, M2 EQ-Bank 9 MC

A hot air balloon contains 65 L of air at ground level, where the conditions are 98 kPa and 27°C.

What will be the new volume of the balloon when it rises to an altitude where the conditions are 10 kPa and –10°C?

  1. 400 L
  2. 484 L
  3. 558 L
  4. 610 L
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\(C\)

Show Worked Solution
  • Using the Combined Gas Law: \(\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}\)
  •    \(T_1 = 300\ \text{K}\)  and  \(T_2 = 263\ \text{K}\)
  •    \(V_2=\dfrac{P_1V_1T_2}{T_1P_2}=\dfrac{98 \times 65 \times 263}{300 \times 10}=558\ \text{L}\)

\(\Rightarrow C\)

CHEMISTRY, M2 EQ-Bank 10

A sample of nitrogen gas at a pressure of 400 kPa and a temperature of 60.0°C occupies a volume of 35.0 L.

  1. Calculate the volume of this nitrogen gas at 298 K and 120 kPa.   (3 marks)
  1. Calculate the number of moles of nitrogen in this sample.   (2 marks)
  1. Calculate the mass of this nitrogen sample.   (2 marks)
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a.    \(104.4\ \text{L}\)

b.    \(5.06\ \text{mol}\)

c.    \(141.8\ \text{g}\)

Show Worked Solution

a.    Using the Combined Gas Law: \(\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}\)

\(T_1 = 60^{\circ}\text{C}=333\ \text{K}\)

\(V_2=\dfrac{P_1V_1T_2}{T_1P_2}=\dfrac{400 \times 35 \times 298}{333 \times 120}=104.4\ \text{L}\)

 

b.    Using the Ideal Gas Law: \(PV=nRT\) 

\(n=\dfrac{PV}{RT}=\dfrac{400 \times 35}{8.314 \times 333}=5.06\ \text{mol}\)

 

c.    Nitrogen gas \(\ce{(N2)}\) has a molar mass of \(28.02\ \text{g mol}^{-1}\)

\(\ce{m(N2)}= n \times MM = 5.06 \times 28.02 = 141.8\ \text{g}\)

CHEMISTRY, M2 EQ-Bank 4 MC

A sample of gas is stored in a container at a pressure of 4.00 kPa, a temperature of 280 K, and a volume of 8.00 L. If the temperature increases to 320 K and the pressure changes to 4.50 kPa, what will the volume be?

  1. \(7.9\ \text{L}\)
  2. \(8.1\ \text{L}\)
  3. \(6.2\ \text{L}\)
  4. Unchanged
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\(B\)

Show Worked Solution
  • Using the Combined Gas Law: \(\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}\)
\(V_2\) \(=\dfrac{P_1 \times V_1 \times T_2}{T_1 \times P_2}\)  
  \(=\dfrac{4.00 \times 8 \times 320}{280 \times 4.5}\)  
  \(=8.1\ \text{L}\)  

 
\(\Rightarrow B\)