Let's say that you are asked to design an airbag for a car. You know that the bag should be filled with gas with a pressure higher than atmospheric pressure, say 828 mmHg at a temperature of 22.0 C . THe bag has a volume of 45.51. What quantity of sodium azide should be used to generate the required quantity of gas?
Use PV = nRT, substitute the values and solve for n = number of mols.
Then write the equation and balance it, plug in the number of mols N2 needed, and use stoichiometry to calculate the quantity of NaN3. If you need help with some of this post the work as far as you can work the problem, then explain in detail what you don't understand about the next step.
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To calculate the quantity of sodium azide needed to generate the required quantity of gas, we can use the ideal gas law and the known conditions provided.
The ideal gas law equation is:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, let's convert the given pressure from mmHg to atmospheres:
828 mmHg = 828 / 760 atm ≈ 1.089 atm
Next, let's convert the given temperature from Celsius to Kelvin:
22 °C + 273.15 = 295.15 K
Now we have the following known values:
P = 1.089 atm
V = 45.51 L
R = 0.0821 L·atm/mol·K
T = 295.15 K
Substituting these values into the ideal gas law equation:
1.089 atm * 45.51 L = n * 0.0821 L·atm/mol·K * 295.15 K
Simplifying:
49.61239 = n * 24.242815
Dividing both sides by 24.242815:
n = 49.61239 / 24.242815 ≈ 2.04 moles
Now, to find the quantity of sodium azide needed, we need to know the molar mass of sodium azide. The molar mass of sodium azide (NaN3) is:
22.99 g/mol (sodium) + 3 * 14.01 g/mol (nitrogen) = 65.01 g/mol
Multiplying the number of moles by the molar mass:
2.04 moles * 65.01 g/mol ≈ 132.40 g
Therefore, approximately 132.40 grams of sodium azide should be used to generate the required quantity of gas.
To calculate the quantity of sodium azide required to generate the required quantity of gas, we need to consider the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
Now, let's begin by converting the given pressure from mmHg to atm:
828 mmHg * (1 atm / 760 mmHg) ≈ 1.089 atm
Next, convert the given temperature from Celsius to Kelvin:
22.0°C + 273.15 = 295.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substituting the given values:
n = (1.089 atm) * (45.51 L) / (0.0821 L·atm/(mol·K) * 295.15 K)
Performing the calculation gives us the number of moles of gas:
n ≈ 1.759 moles (rounded to three decimal places)
To determine the quantity of sodium azide needed, we need to know the stoichiometry between sodium azide and the gas being generated. Without this information, it is not possible to calculate the exact quantity of sodium azide required.