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Question 4: (answer in place of item 17)
2 moles of Sodium Azide (NaN,) produces about 3 moles of Nitrogen (N,) in a car's airbag.
How many moles of NaN, are needed to fill a 65 L airbag? Assume the gas is produced at a temperature of 30 °C and 2.5 atm.
To calculate the number of moles of NaN3 needed to fill a 65 L airbag, we can use the ideal gas law equation: PV = nRT.
Given:
Temperature (T) = 30 °C = 30 + 273.15 = 303.15 K
Pressure (P) = 2.5 atm
Volume (V) = 65 L
R = 0.0821 L·atm/(K·mol) (ideal gas constant)
We can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Plugging in the values:
n = (2.5 atm) x (65 L) / (0.0821 L·atm/(K·mol) x 303.15 K)
Calculating this equation will give us the number of moles of NaN3 needed to fill the 65 L airbag.
To solve this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperature from Celsius to Kelvin. The conversion formula is K = °C + 273.15. So, 30 °C + 273.15 = 303.15 K.
Now we can rearrange the ideal gas law to solve for the number of moles:
n = PV / RT
Given:
P = 2.5 atm
V = 65 L
T = 303.15 K
We also need the ideal gas constant, which is R = 0.0821 L·atm/(mol·K).
Plugging in the values, we get:
n = (2.5 atm)(65 L) / (0.0821 L·atm/(mol·K))(303.15 K)
n ≈ 184.85 moles
Therefore, you would need approximately 184.85 moles of NaN3 to fill a 65 L airbag at a temperature of 30 °C and a pressure of 2.5 atm.
To solve this problem, we need to use the ideal gas law equation, which is:
PV = nRT
Where:
P is the pressure in atm (2.5 atm),
V is the volume in liters (65 L),
n is the number of moles of gas we want to find,
R is the ideal gas constant (0.0821 L.atm/mol.K), and
T is the temperature in Kelvin (30°C + 273 = 303 K).
Rearranging the equation to solve for n, we have:
n = PV / RT
n = (2.5 atm) * (65 L) / (0.0821 L.atm/mol.K * 303 K)
n ≈ 59.93 moles
Therefore, approximately 60 moles of NaN3 are needed to fill a 65 L airbag.