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CHEMISTRY, M2 EQ-Bank 11

Iron forms a compound that contains iron (36.8%), sulfur (31.6%), and oxygen (31.6%). The compound boils at 120°C. For one mole of this compound, the density of its vapor at 150°C and 250 kPa is 42.0 g/L.

  1. Determine the empirical formula of the compound.   (2 mark)
  1. Calculate the molar mass of the compound.   (2 marks)
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a.    \(\ce{Fe2S3O6}\)

b.    \(590.94\ \text{g mol}^{-1}\).

Show Worked Solution

a.   Divide each compound’s percentage by their molar masses:

\(\ce{Fe}: \dfrac{36.8%}{55.85} = 0.65 \ \Rightarrow \ \dfrac{0.659}{0.659}=1\)

\(\ce{S}: \dfrac{31.6%}{32.07} = 0.985 \ \Rightarrow \ \dfrac{0.985}{0.659}=\dfrac{3}{2}\)

\(\ce{O}: \dfrac{31.6%}{16.00} = 1.975 \ \Rightarrow \ \dfrac{1.975}{0.659}=3\)

  • Due to the fraction, each number must be doubled so there are only whole numbers.
  • Thus the empirical formula for the compound is \(\ce{Fe2S3O6}\).

b.    Using the Ideal Gas Law to find the volume of the vapour:

\(V=\dfrac{nRT}{P}=\dfrac{1 \times 8.314 \times (150+273)}{250}=14.07\ \text{L}\)

  • Molar mass of the vapour \(= 42 \times 14.07 = 590.94\ \text{g mol}^{-1}\).

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 8

A gas at a temperature of \(9.0 \times 10^2\ \text{K}\) in a container with a volume of \(30.0\ \text{L}\) has a pressure of \(5.0 \times 10^2\ \text{kPa}\).

  1. How many moles of gas are in the container?   (3 marks)
  1. If the empty container weighs \(450.0\ \text{g}\) and the container with the gas weighs \(526.0\ \text{g}\), what is the gaseous element in the container?   (2 marks)
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a.    \(2.0\ \text{mol}\)

b.    The unknown gas is fluorine.

Show Worked Solution

a.    Using the Ideal Gas Law:

\(PV=nRT \Rightarrow n=\dfrac{PV}{RT}\)

\(n=\dfrac{500 \times 30}{8.314 \times 900}=2.0\ \text{mol (2 sig.fig)}\) 

 

b.    Mass of the gas \(=526.0-450.0=76\ \text{g}\)

Molar Mass of the gas \(=\dfrac{m}{n}=\dfrac{76}{2.0}=38\ \text{g mol}^{-1}\)

  • This is equal to the MM of fluorine gas \(\ce{(F2)}\).
  • The unknown gas is fluorine.

CHEMISTRY, M2 EQ-Bank 5 MC

Which of the following best describes the properties of an ideal gas?

  1. The molecules do not attract each other and occupy a negligible volume.
  2. The molecules experience strong repulsive forces and expand to fill the container.
  3. The gas particles have significant mass and their collisions reduce total energy.
  4. The pressure of the gas depends on the chemical identity of the particles.
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\(A\)

Show Worked Solution
  • An ideal gas is defined by the assumption that its molecules have no intermolecular forces and occupy negligible volume relative to the container.
  • The gas particles are in constant random motion, and collisions between them are perfectly elastic, meaning no kinetic energy is lost.

\(\Rightarrow A\)

CHEMISTRY, M2 EQ-Bank 3 MC

What volume will 3.0 mol of oxygen occupy at 200°C and 150 kPa?

  1. 33.3 L
  2. 52.8 L
  3. 62.4 L
  4. 78.6 L
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\(D\)

Show Worked Solution
  • Using the Ideal Gas Law, \(PV=nRT \ \Rightarrow \ V=\dfrac{nRT}{P}\)
  •    \(V=\dfrac{3.0 \times 8.314 \times (200 + 273)}{150}=78.6\ \text{L}\)

\(\Rightarrow D\)