Calculate how many grams of sodium azide (NaN3) are needed to inflate a 25.0 × 25.0 × 20.0 cm bag to a pressure of 1.25 atm at a temperature of 20.0°C. How much sodium azide is needed if the air bag must produce the same pressure at 10.0°C?
20.0°C:
_______ g NaN3
Were you given an equation for the decomposition? If so, make sure it agrees with what I've written; otherwise I will use this one.
2NaN3 ==> 2Na + 3N2
volume of bag is 25 x 25 x 20 = approx approx 13,000 cc or about 13 L but you need a better answer than this estimate. All numbers below this one are estimates also.
Use PV = nRT. You know P, V, R and T (must be in kelvin). Solve for n = mols. That will be mols N2.
Use the coefficients in the balanced equation to convert mols N2 to mols NaN3. You can see that 3 mols N2 need 2 mols NaN3.
Then grams NaN3 = mols NaN3 x molar mass NaN3.
Do the same procedure for the second part of the problem.
Post your work if you get stuck.
To calculate the number of grams of sodium azide (NaN3) needed to inflate the bag to a certain pressure, we need to use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure in atmospheres (atm)
- V is the volume in liters (L)
- n is the number of moles of gas
- R is the ideal gas constant (0.0821 L·atm/mol·K)
- T is the temperature in Kelvin (K)
First, let's convert the given temperature from Celsius to Kelvin:
20.0°C + 273.15 = 293.15 K
Next, let's calculate the initial number of moles of NaN3:
We know the volume of the bag is given as 25.0 cm × 25.0 cm × 20.0 cm, which is equal to 12,500 cm³ or 12.5 L.
Now we can rearrange the ideal gas law equation to solve for n:
n = PV / RT
Substituting the given values:
n = (1.25 atm) × (12.5 L) / (0.0821 L·atm/mol·K) × (293.15 K)
Simplifying this equation gives us the initial number of moles of NaN3.
Finally, to find the mass of NaN3, we need to multiply the number of moles by its molar mass. The molar mass of NaN3 is calculated by summing the atomic masses of sodium (Na) and nitrogen (N) three times:
Molar mass of NaN3 = (22.99 g/mol) + (14.01 g/mol * 3) = _______ g/mol
To calculate the mass of NaN3 needed, multiply the number of moles by the molar mass.
Therefore, to determine the mass of NaN3 needed to inflate the bag at 20.0°C, you would need to use the above calculations and:
- Calculate the initial number of moles of NaN3 using the ideal gas law equation.
- Calculate the molar mass of NaN3.
- Multiply the number of moles by the molar mass to obtain the mass of NaN3 needed.