A piece of Na metal undergoes a complete reaction with H2O (l0 to produce sodium hydroxide and hydrogen. If 24.0 g of Na in a 3.50 L container is reacted with an excess amount of water at 25 degrees Celsius, calculate the total pressure (in atm) in the 3.50 L container when the reaction is completed. (The vapor pressure of H2O at 25 degrees Celsius = 23.8 mm Hg)
To calculate the total pressure in the 3.50 L container after the reaction is completed, we need to take into account the hydrogen gas produced as well as the water vapor in the container.
First, let's convert the mass of Na metal given (24.0 g) to moles by dividing it by the molar mass of sodium (22.99 g/mol).
24.0 g Na / 22.99 g/mol ≈ 1.04 mol Na
The balanced chemical equation for the reaction between Na and water is:
2 Na + 2 H2O -> 2 NaOH + H2
From the balanced equation, we can see that for every 2 moles of Na, we get 1 mole of H2.
Therefore, the number of moles of hydrogen gas produced is half the number of moles of sodium:
1.04 mol Na * (1 mol H2 / 2 mol Na) = 0.52 mol H2
Now, let's consider the water vapor. Since the reaction is carried out in excess water, we can assume that all of the water is converted to water vapor.
The vapor pressure of water at 25 degrees Celsius is given as 23.8 mm Hg. To convert this to atm, we divide by 760 (since 760 mm Hg is the standard atmospheric pressure):
23.8 mm Hg / 760 mm Hg/atm ≈ 0.0313 atm
Since the total pressure is the sum of the partial pressures of all the gases in the container, we can calculate the total pressure using the ideal gas law:
Ptotal = PH2 + PH2O
PH2 = nH2 * RT / V (where nH2 is the number of moles of H2, R is the ideal gas constant, T is the temperature in Kelvin, and V is the volume)
PH2O = PV / RT (where P is the vapor pressure, V is the volume, R is the ideal gas constant, and T is the temperature in Kelvin)
Let's substitute the values into the equations:
PH2 = (0.52 mol) * (0.0821 L·atm/mol·K) * (25 + 273 K) / 3.50 L
PH2 ≈ 2.52 atm
PH2O = (0.0313 atm) * (3.50 L) / (0.0821 L·atm/mol·K) * (25 + 273 K)
PH2O ≈ 2.18 atm
Ptotal = 2.52 atm + 2.18 atm
Ptotal ≈ 4.70 atm
Therefore, the total pressure in the 3.50 L container when the reaction is completed is approximately 4.70 atm.