Answer:
Step-by-step explanation:
To calculate the mass of sodium azide needed to fill a 48dm³ air bag with gas at r.t.p., you need to use the ideal gas law. The ideal gas law states that the pressure of a gas is directly proportional to its temperature (in Kelvins) and the number of moles of gas present, and inversely proportional to its volume. The ideal gas law can be expressed as:
PV = nRT
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of the gas
- R is the ideal gas constant
- T is the temperature of the gas
You can rearrange the ideal gas law to solve for the number of moles of gas present:
n = PV / RT
To solve this problem, you need to plug in the known values. At r.t.p., the pressure is 1 atm, the temperature is 273 K, and the volume is 48 dm³. The ideal gas constant is 8.31 J/mol*K. Plugging in these values, you get:
n = (1 atm * 48 dm³) / (8.31 J/mol*K * 273 K)
Solving for n, you get:
n = 0.0174 moles
Now that you have the number of moles of gas present, you can use the balanced chemical equation for the decomposition of sodium azide to calculate the number of moles of sodium azide needed. The balanced chemical equation is:
2 NaN3 (s) → 2 Na(s) + 3 N₂ (g)
This equation tells you that for every 2 moles of sodium azide that decompose, you get 3 moles of nitrogen gas. Since you need 0.0174 moles of nitrogen gas, you can divide that number by 3 to get the number of moles of sodium azide needed:
0.0174 moles N₂ / 3 moles N₂/2 moles NaN3 = 0.0087 moles NaN3
To convert the number of moles to mass, you need to know the molar mass of sodium azide. The molar mass of sodium azide is 65.01 g/mol. Plugging in the number of moles and the molar mass, you get:
0.0087 moles NaN3 * 65.01 g/mol = 0.5686 g NaN3
So, the mass of sodium azide needed to fill a 48dm³ air bag with gas at r.t.p. is approximately 0.5686 grams.