SSCE HSC Chemistry Chemical Reactions and Stoichiometry: Sodium azide is used in automobi

Sodium azide is used in automobile airbags to provide a source of nitrogen gas for rapid inflation in an accident - HSC - SSCE Chemistry - Question 19 - 2010 - Paper 1

Question 19

Sodium azide is used in automobile airbags to provide a source of nitrogen gas for rapid inflation in an accident. The equation shows the production of nitrogen gas ... show full transcript

Worked Solution & Example Answer:Sodium azide is used in automobile airbags to provide a source of nitrogen gas for rapid inflation in an accident - HSC - SSCE Chemistry - Question 19 - 2010 - Paper 1

Step 1

Convert Volume of Nitrogen Gas to Moles

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Answer

To find the number of moles of nitrogen gas produced, we can use the Ideal Gas Law: $PV = nRT$ Where:

P = pressure (100 kPa)
V = volume (40 L)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (273 K for 0°C)

First, convert pressure from kPa to Pa: 100 kPa = 100,000 Pa.

Now, rearranging the ideal gas law: $n = \frac{PV}{RT}$ Substituting in the values: $n = \frac{(100,000 Pa)(40 L)}{(8.314 J/(mol·K))(273 K)}$

Calculating: $n \approx 1.77 mol$

Step 2

Determine Moles of Sodium Azide Required

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Answer

From the balanced equation: $2NaN_3 \rightarrow 3N_2$ It shows that 2 moles of sodium azide produce 3 moles of nitrogen gas. Therefore, we can set up a ratio: $\frac{2 \text{ moles of } NaN_3}{3 \text{ moles of } N_2} = \frac{x \text{ moles of } NaN_3}{1.77 \text{ moles of } N_2}$

Cross-multiplying gives: $x = \frac{2}{3} \times 1.77 \approx 1.18 \text{ moles of } NaN_3$

Step 3

Convert Moles of Sodium Azide to Mass

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Answer

Now, we need to find the mass of sodium azide. The molar mass of sodium azide (NaN₃) can be calculated as:

Na: 22.99 g/mol
N: 14.01 g/mol
Total: 22.99 + (3 x 14.01) = 65.01 g/mol

To find the mass, we use the formula: $mass = n \times molar \ mass$ Substituting in our values: $mass = 1.18 ext{ moles} \times 65.01 \text{ g/mol} \approx 76.7 g$

Thus, the answer rounds to 76 g.

Sodium azide is used in automobile airbags to provide a source of nitrogen gas for rapid inflation in an accident - HSC - SSCE Chemistry - Question 19 - 2010 - Paper 1

Worked Solution & Example Answer:Sodium azide is used in automobile airbags to provide a source of nitrogen gas for rapid inflation in an accident - HSC - SSCE Chemistry - Question 19 - 2010 - Paper 1

Convert Volume of Nitrogen Gas to Moles

Determine Moles of Sodium Azide Required

Convert Moles of Sodium Azide to Mass

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