When 1.675grams of hydrated sodium carbonate was reacted with excess hydrochloric acid the volume carbon iv oxide gas obtained at room temperature and pressure was 150 calculate the number of moles of water of crystalization in one mole of hydrated sodium carbonate
The first step is to calculate the number of moles of carbon dioxide gas produced:
1. Convert the mass of sodium carbonate to moles:
1.675 g Na2CO3 * (1 mol Na2CO3 / 105.99 g Na2CO3) = 0.0158 mol Na2CO3
2. Since there is excess hydrochloric acid, all of the Na2CO3 will react to produce CO2:
Na2CO3 + 2HCl → CO2 + H2O + 2NaCl
3. From the balanced equation, 1 mole of Na2CO3 produces 1 mole of CO2:
0.0158 mol Na2CO3 → 0.0158 mol CO2
So the number of moles of CO2 produced is 0.0158.
Now we can use the ideal gas law to calculate the volume of CO2 produced:
PV = nRT
where P is the pressure (1 atm), V is the volume (150 L), n is the number of moles (0.0158), R is the gas constant (0.082 L·atm/K·mol), and T is the temperature (room temperature, which we'll assume is 298 K).
Solving for V, we get:
V = nRT/P = (0.0158 mol)(0.082 L·atm/K·mol)(298 K)/(1 atm) = 0.385 L
So the volume of CO2 produced is actually 0.385 L, not 150 L. This suggests there may be an error in the problem statement.
Assuming that the correct volume of CO2 is indeed 0.385 L, we can now calculate the number of moles of water of crystallization in one mole of hydrated sodium carbonate. Here's the balanced equation for the reaction of hydrated sodium carbonate with hydrochloric acid:
Na2CO3·xH2O + 2HCl → CO2 + H2O + 2NaCl + xH2O
The coefficient of H2O in this equation tells us how many moles of water are released per mole of hydrated sodium carbonate. Since the problem is asking for the number of moles of water of crystallization (i.e. the number of moles of water per mole of hydrated sodium carbonate), we need to divide the coefficient by x.
Looking at the equation, we see that 1 mole of hydrated sodium carbonate produces 1 mole of CO2 and x moles of water. From the previous calculations, we know that 0.0158 moles of hydrated sodium carbonate produced 0.385 L of CO2. Since 1 mole of CO2 occupies 22.4 L at room temperature and pressure, the volume of 0.385 L corresponds to:
0.385 L CO2 * (1 mol CO2 / 22.4 L CO2) = 0.0172 mol CO2
Since 1 mole of hydrated sodium carbonate produces 1 mole of CO2, we know that 0.0158 moles of hydrated sodium carbonate produced 0.0172 moles of CO2. Therefore, the number of moles of water released per mole of hydrated sodium carbonate is:
xH2O / 1 mol Na2CO3 = 0.0172 mol CO2 / 0.0158 mol Na2CO3
Solving for x, we get:
x = 1.09
So the number of moles of water of crystallization in one mole of hydrated sodium carbonate is approximately 1.09.