To calculate the volume of nitrogen gas generated, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles (in mol)
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
First, let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15 = 21 + 273.15 = 294.15 K
Next, we need to calculate the number of moles of nitrogen gas generated. From the balanced equation for the decomposition of sodium nitrate:
2NaNO3 → 2NaNO2 + O2
we can see that for every 2 moles of sodium nitrate, we get 1 mole of nitrogen gas. So, we first need to find the number of moles of sodium nitrate.
Molar mass of NaNO3:
Na = 22.99 g/mol
N = 14.01 g/mol
O = 16.00 g/mol
Total molar mass = (22.99 g/mol + 14.01 g/mol + 3 * 16.00 g/mol) = 85.00 g/mol
Now, we can calculate the number of moles of sodium nitrate:
n = mass / molar mass = 60.0 g / 85.00 g/mol = 0.706 mol
Since 2 moles of sodium nitrate yield 1 mole of nitrogen gas, the number of moles of nitrogen gas is also 0.706 mol.
Finally, we can now use the ideal gas law to calculate the volume of nitrogen gas generated:
PV = nRT
V = nRT / P
= (0.706 mol)(0.0821 L.atm/mol.K)(294.15 K) / (823 mmHg / 760 mmHg/atm)
≈ 0.160 L (rounded to three decimal places)
Therefore, the volume of nitrogen gas generated is approximately 0.160 liters.