To calculate the mass of sodium azide needed to produce 144 dm^3 of nitrogen, we first need to calculate the number of moles of nitrogen.
Step 1: Calculate the number of moles in 144 dm^3 of nitrogen at room temperature and pressure.
Using the ideal gas equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature:
Assuming room temperature is 25 degrees Celsius or 298 Kelvin and pressure is 1 atmosphere, we have:
P = 1 atm
V = 144 dm^3
T = 298 K
R = 0.0821 L.atm/mol.K (ideal gas constant)
Using the ideal gas equation, we can solve for n:
n = PV/RT
n = (1 atm) * (144 dm^3) / (0.0821 L.atm/mol.K * 298 K)
n = 6.16 moles of N2
Step 2: Determine the number of moles of Na*N_{3} needed to produce 6.16 moles of N2.
From the balanced chemical equation, we see that 2 moles of Na*N_{3} produce 3 moles of N2.
Using this ratio, we can set up a proportion to find the number of moles of Na*N_{3} needed:
2 moles Na*N_{3} / 3 moles N2 = x moles Na*N_{3} / 6.16 moles N2
Solving for x:
x = (2 moles Na*N_{3} / 3 moles N2) * 6.16 moles N2
x = 4.107 moles Na*N_{3}
Step 3: Calculate the relative formula mass, M_N* of Na*N_{3}.
The relative formula mass is the sum of the atomic masses of all the atoms in the formula.
Na*N_{3} contains 1 sodium (Na) atom, which has an atomic mass of 22.99 g/mol,
and 3 nitrogen (N) atoms, which have an atomic mass of 14.01 g/mol each.
M_N* = (1 Na * 22.99 g/mol) + (3 N * 14.01 g/mol)
M_N* = 66.03 g/mol
Step 4: Calculate the mass of Na*N_{3} needed to produce 144 dm^3 of N2.
Using the mole-mass relationship, where mass = moles * molar mass:
Mass of Na*N_{3} = moles of Na*N_{3} * M_N*
Mass of Na*N_{3} = 4.107 moles * 66.03 g/mol
Mass of Na*N_{3} = 271.07 g
Therefore, the mass of sodium azide needed to produce 144 dm^3 of nitrogen is 271.07 grams.
(b) Some car airbags contain sodium azide. When a car airbag is used the sodium azide, Na*N_{3} decomposes. The products are nitrogen and sodium.
The equation for the decomposition of sodium azide is shown.
2Na*N_{3}(s) -> 2Na(l) + 3N_{2}(g)
Calculate the mass, in g. of sodium azide needed to produce 144d * m ^ 3 of nitrogen using the following steps.
Calculate the number of moles in 144d * m ^ 3 of N_{2} measured at room temperature and pressure.
Determine the number of moles of Na*N_{3} needed to produce this number of moles of N_{2}
⚫ Calculate the relative formula mass, M_{n}*ofNa*N_{3}
moiesofNa*N_{3} =
M =\
Calculate the mass of Na*N_{3} needed to produce 144d * m ^ 3 of N_{2}
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