Automotive airbags inflate when sodium azide, NaN3, rapidly decomposes to its constituent elements according to the chemical equation, 2 NaN3 -> 2 Na + 3 N2. How many grams of nitrogen are produced when 1000 milligrams of sodium azide decomposes?
2NaN3 -> 2Na + 3N2.
mols NaN3 = grams/molar mass
Using the coefficients in the balanced equation, convert mols NaN3 to mols N2
Finally, convert mols N2 to grams. g N2 = mols N2 x molar mass N2.
Automotive airbags inflate when sodium azide, NaN3, rapidly decomposes to its constituent elements according to the chemical equation, 2 NaN3 -> 2 Na + 3 N2. How many grams of nitrogen are produced when 1000 milligrams of sodium azide decomposes?
To determine the number of grams of nitrogen produced when 1000 milligrams of sodium azide decomposes, we need to use stoichiometry.
Given:
Mass of sodium azide (NaN3) = 1000 milligrams
First, we need to convert the mass of sodium azide from milligrams to grams since the molar mass of NaN3 is expressed in grams.
1 gram = 1000 milligrams
So, 1000 milligrams = 1 gram.
Next, we need to convert the mass (in grams) of NaN3 to moles of NaN3. To do this, we use the molar mass of NaN3.
Molar mass of NaN3:
Na = 22.99 g/mol
N = 14.01 g/mol
3(14.01) = 42.03 g/mol
Molar mass of NaN3 = 22.99 + 42.03 = 65.02 g/mol
Now, we can convert the mass of NaN3 to moles using the relationship:
moles of NaN3 = mass of NaN3 (in grams) / molar mass of NaN3
moles of NaN3 = 1 gram / 65.02 g/mol
Next, we can use the stoichiometry of the reaction to determine the moles of nitrogen produced. According to the balanced equation:
2 NaN3 -> 2 Na + 3 N2
We can see that 2 moles of NaN3 produce 3 moles of N2.
moles of N2 = (moles of NaN3) x (3 moles of N2 / 2 moles of NaN3)
Finally, to find the mass of nitrogen produced, we can use the molar mass of nitrogen:
Molar mass of N2 = 2(14.01) = 28.02 g/mol
mass of N2 (in grams) = moles of N2 x molar mass of N2
Therefore, to find the mass of nitrogen produced when 1000 milligrams of sodium azide decomposes, we need to perform the following calculations:
1. Convert milligrams to grams: 1000 milligrams = 1 gram
2. Calculate the moles of NaN3: 1 gram / 65.02 g/mol
3. Use stoichiometry to calculate the moles of N2: (moles of NaN3) x (3 moles of N2 / 2 moles of NaN3)
4. Calculate the mass of N2: moles of N2 x molar mass of N2.
To find the number of grams of nitrogen produced when 1000 milligrams of sodium azide decomposes, we can use stoichiometry.
First, we need to calculate the molar mass of sodium azide (NaN3). Sodium (Na) has a molar mass of 22.99 g/mol, and nitrogen (N) has a molar mass of 14.01 g/mol. The molar mass of NaN3 can be calculated as follows:
Molar mass of NaN3 = (Molar mass of Na) + 3 x (Molar mass of N)
= 22.99 g/mol + 3 x 14.01 g/mol
= 65.03 g/mol
Now, let's use the molar mass of NaN3 to convert the given mass of sodium azide (1000 milligrams) to moles. To do this, we'll use the equation:
moles = mass / molar mass
moles of sodium azide = 1000 mg / (65.03 g/mol)
= 0.0154 mol
According to the balanced chemical equation, 2 moles of NaN3 produce 3 moles of nitrogen gas (N2).
Therefore, if 0.0154 mol of sodium azide decomposes, the number of moles of nitrogen gas produced can be calculated using the stoichiometric ratio:
moles of nitrogen = 3/2 x moles of sodium azide
= 3/2 x 0.0154 mol
= 0.0231 mol
Finally, we can convert the moles of nitrogen gas to grams using the molar mass of nitrogen (N), which is 14.01 g/mol:
grams of nitrogen = moles of nitrogen x molar mass of nitrogen
= 0.0231 mol x 14.01 g/mol
= 0.323 g
Therefore, when 1000 milligrams of sodium azide decompose, approximately 0.323 grams of nitrogen gas are produced.