To find the answer to these questions, we will need to use the concept of molarity and stoichiometry. Molarity, represented by the symbol M, is a measure of the concentration of a solute in a solution. It is defined as the amount of substance (in moles) divided by the volume of the solution (in liters). The formula for calculating molarity is:
Molarity (M) = moles of solute / volume of solution (in liters)
To solve the given problem, we will follow these steps:
Step 1: Convert the given volume of solutions to liters.
- 100 mL = 100/1000 = 0.1 L
- 200 mL = 200/1000 = 0.2 L
Step 2: Calculate the moles of K3BO3.
- Given concentration of K3BO3 = 0.60 mol/L
- Moles of K3BO3 = concentration * volume
- Moles of K3BO3 = 0.60 mol/L * 0.1 L
- Solution: Moles of K3BO3 = 0.06 mol (a)
Step 3: Calculate the moles of Ca3(BO3)2.
- Given concentration of Ca3(BO3)2 = 0.40 mol/L
- Moles of Ca3(BO3)2 = concentration * volume
- Moles of Ca3(BO3)2 = 0.40 mol/L * 0.2 L
- Solution: Moles of Ca3(BO3)2 = 0.08 mol (b)
Step 4: Calculate the final concentrations.
- Since we are mixing two solutions, the total volume of the final solution is equal to the sum of the volumes of the individual solutions.
- Total volume of final solution = 0.1 L + 0.2 L = 0.3 L
To calculate the final concentration, we will divide the moles of the solute by the total volume of the solution.
(a) Final concentration of K+:
- Divide the moles of K3BO3 by the total volume of the solution.
- Concentration of K+ = moles of K3BO3 / total volume of solution
- Concentration of K+ = 0.06 mol / 0.3 L
- Solution: Final concentration of K+ = 0.20 mol/L (c)
(b) Final concentration of Ca+2:
- Divide the moles of Ca3(BO3)2 by the total volume of the solution.
- Concentration of Ca+2 = moles of Ca3(BO3)2 / total volume of solution
- Concentration of Ca+2 = 0.08 mol / 0.3 L
- Solution: Final concentration of Ca+2 = 0.27 mol/L (d)
(c) Final concentration of BO3-3:
- The number of moles of BO3-3 is the same as the number of moles of Ca3(BO3)2 since the ratio is 1:1.
- Concentration of BO3-3 = moles of Ca3(BO3)2 / total volume of solution
- Concentration of BO3-3 = 0.08 mol / 0.3 L
- Solution: Final concentration of BO3-3 = 0.27 mol/L (e)
To recap:
(a) Moles of K3BO3 = 0.06 mol
(b) Moles of Ca3(BO3)2 = 0.08 mol
(c) Final concentration of K+ = 0.20 mol/L
(d) Final concentration of Ca+2 = 0.27 mol/L
(e) Final concentration of BO3-3 = 0.27 mol/L