Nitrogen gas and sodium liquid are produced by the decomposition of sodium azide NaN3 (s). what volume of nitrogen gas, measured at 25 C and 0.980 atm, is produced by the decomposition of 62.5 g of sodium azide
Write the equation and balance it.
Convert 62.5 g NaN3 to mols. mol = g/molar mass.
Use the coefficients to convert mols NaN3 to mols N2 gas.
Use PV = nRT to convert n to volume at the conditions listed.
To solve this problem, we need to use the molar mass of sodium azide (NaN3) and the ideal gas law equation.
1. Calculate the number of moles of sodium azide (NaN3):
Molar mass of NaN3 = 22.99 g/mol (Na) + 3 × 14.01 g/mol (N) = 65.01 g/mol
Number of moles of NaN3 = Mass of NaN3 / Molar mass of NaN3 = 62.5 g / 65.01 g/mol = 0.9612 mol
2. Determine the stoichiometry between NaN3 and N2:
From the balanced chemical equation, we know that 2 moles of NaN3 decompose to produce 3 moles of N2.
Therefore, 0.9612 mol of NaN3 will produce (0.9612 mol * 3 mol) / 2 mol = 1.4418 mol of N2.
3. Apply the ideal gas law equation: PV = nRT
R = 0.0821 L·atm/mol·K (the ideal gas constant)
T = 25 °C = 25 + 273.15 = 298.15 K (convert to Kelvin)
P = 0.980 atm (given pressure)
V = nRT / P
V = (1.4418 mol) * (0.0821 L·atm/mol·K) * (298.15 K) / (0.980 atm)
V ≈ 36.09 L
Therefore, approximately 36.09 liters (L) of nitrogen gas will be produced by the decomposition of 62.5 grams of sodium azide at 25 °C and 0.980 atm.
To find the volume of nitrogen gas produced by the decomposition of sodium azide, we need to use the ideal gas law. The ideal gas law equation is:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L atm/(mol K))
T = temperature (in Kelvin)
First, we need to find the number of moles of sodium azide. To do this, we'll use the molar mass of sodium azide (NaN3), which is the sum of the molar masses of its constituent elements:
Molar mass of sodium (Na) = 23 g/mol
Molar mass of nitrogen (N) = 14 g/mol
Molar mass of sodium azide (NaN3) = Molar mass of sodium (Na) + 3 × Molar mass of nitrogen (N)
Molar mass of sodium azide (NaN3) = 23 g/mol + 3 × 14 g/mol = 65 g/mol
Now, let's calculate the number of moles of sodium azide:
Number of moles = mass / molar mass
Number of moles = 62.5 g / 65 g/mol
Next, we can calculate the volume of nitrogen gas using the ideal gas law. Before we do that, we need to convert the temperature from Celsius to Kelvin:
Temperature (Kelvin) = 25°C + 273.15
Then we can substitute the values into the ideal gas law equation to solve for the volume:
V = (nRT) / P
V = (number of moles × ideal gas constant × temperature) / pressure
Finally, let's substitute the values and solve for the volume:
V = (number of moles × 0.0821 L atm/(mol K) × temperature (Kelvin)) / pressure
Once you have calculated V, you will have the volume of nitrogen gas produced by the decomposition of sodium azide.