The equation for the reaction of sodium with water is as follows:
2Na(s) �2H2O(l) £ H2(g) �2NaOH(aq)
How many liters of H2 are produced when 12.0 g of Na reacts with H2O at
293 K and 99.3 kPa?
Convert 12.0 g Na to moles. moles = grams/molar mass.
Using the coefficients in the balanced equation, convert moles Na to moles H2.
Use PV = nRT with p in atm, n is moles, and T in Kelvin to determine volume in L.
To find the number of liters of H2 gas produced, we need to follow a series of steps:
1. Determine the moles of Na used:
- Convert the given mass of Na (12.0 g) to moles by dividing by the molar mass of Na (22.99 g/mol).
- molar mass of Na = 22.99 g/mol
Calculation:
Moles of Na = 12.0 g / 22.99 g/mol
2. Use the stoichiometric coefficients from the balanced chemical equation to determine the moles of H2 produced:
- In the balanced equation, the stoichiometric coefficient of Na is 2 (2Na), meaning that 2 moles of Na react to produce 1 mole of H2 gas.
Calculation:
Moles of H2 = (Moles of Na) / 2
3. Apply the ideal gas law to convert moles of H2 gas to liters:
- Use the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
- Rearrange the equation to solve for V: V = nRT / P.
- Given values: T = 293 K (temperature) and P = 99.3 kPa (pressure).
- R, the ideal gas constant, is 0.0821 L·atm/(K·mol), but we need to convert kPa to atm for the unit consistency.
Calculation:
V = (Moles of H2) * (R) * (T) / (P)
P (in atm) = 99.3 kPa / 101.325 kPa/atm
V = (Moles of H2) * (0.0821 L·atm/(K·mol)) * (293 K) / (P)
After performing these calculations, you should have the number of liters of H2 gas produced when 12.0 g of Na reacts with H2O at 293 K and 99.3 kPa.