Automotive airbags inflate when sodium azide decomposes explosively to its constituent elements. How many grams of sodium azide are required to produce 24.4 L of nitrogen gas at standard temperature and pressure? 2NaN3 --> 2Na + 3N2 47.2 g of sodium azide

106.2 g of sodium azide

1.63 g of sodium azide

0.726 g of sodium azide

47.2 g of sodium azide

Explanation:

According to avogadro's law, 1 mole of every substance occupies 22.4 L at STP and contains avogadro's number of particles.

To calculate the moles, we use the equation:

The balanced chemical reaction is:

According to stoichiometry :  

3 moles of are produced by = 2 moles of

Thus 1.09 moles of are produced by =  of

Mass of

Thus 47.2 g of sodium azide are required to produce 24.4 L of nitrogen gas at standard temperature and pressure

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years