You mix 200.0 mL of 0.350 M HCl with a 300.0 mL solution of 0.100 M Ba(OH)2. Calculate the concentration of each ion remaining in the solution after the reaction has reached completion.
To calculate the concentration of each ion remaining in the solution after the reaction has reached completion, we need to first determine the balanced equation for the reaction between HCl and Ba(OH)2.
The balanced chemical equation for the reaction between HCl and Ba(OH)2 is:
2HCl + Ba(OH)2 --> BaCl2 + 2H2O
From the equation, we can see that 2 moles of HCl react with 1 mole of Ba(OH)2 to produce 1 mole of BaCl2 and 2 moles of water.
To start solving the problem, we need to calculate the moles of HCl and Ba(OH)2 in the initial solutions.
Moles of HCl = Volume (in liters) x Molarity
= 200.0 mL x (1 L / 1000 mL) x 0.350 M
= 0.070 mol
Moles of Ba(OH)2 = Volume (in liters) x Molarity
= 300.0 mL x (1 L / 1000 mL) x 0.100 M
= 0.030 mol
According to the balanced equation, 2 moles of HCl react completely with 1 mole of Ba(OH)2. Therefore, the limiting reactant is Ba(OH)2, and all of it will react.
Since 2 moles of HCl react with 1 mole of Ba(OH)2, the number of moles of HCl required to react completely with Ba(OH)2 is half of the moles of Ba(OH)2.
Number of moles of HCl required = 0.030 mol / 2 = 0.015 mol
Since HCl is in excess, the remaining moles of HCl after the reaction is complete is:
Moles of HCl remaining = Initial moles of HCl - Moles of HCl required
= 0.070 mol - 0.015 mol
= 0.055 mol
Now, we can calculate the concentration (Molarity) of each ion remaining in the solution.
For Ba2+ ion (from BaCl2):
Concentration of Ba2+ = Moles of Ba2+ / Volume of solution (in liters)
= 0.030 mol / (0.2 L + 0.3 L) (Volume of both solutions combined)
= 0.03 mol / 0.5 L
= 0.060 M
For Cl- ion (from HCl):
Concentration of Cl- = Moles of Cl- / Volume of solution (in liters)
= Moles of HCl remaining / Total volume of the solution
= 0.055 mol / 0.5 L
= 0.110 M
So, after the reaction has reached completion, the concentration of Ba2+ ion remaining in the solution is 0.060 M, and the concentration of Cl- ion remaining is 0.110 M.