Determine the ionic strength of the solution formed by combining the following two aqueous solutions:
Potassium iodide (aq), KI: 70.0 mL, 0.203 M
Ammonium sulphate (aq), (NH4)2SO4: 35.0 mL, 0.246 M
This is a long and tedious problem. Rather than trying to work it out in detail let me ask you what it is you don't understand. There are several sites on the Internet that give specific instructions how to calculate ionic strength as well as the Debye-Huckel theory.
im not seeming to get the right ans. i used .5(CiZi) but still not working
Why not post your work and I'll find the error.
Did you correct for the M; i.e.(KI) = 0.203 x (70.0/105) = ?M
and [(NH4)2SO4] = 0.246 x (35.0/105) = ?M
To determine the ionic strength of a solution formed by combining different solutions, we need to first calculate the total concentration of ions in the combined solution. Ionic strength is a measure of the total concentration of ions in a solution.
Step 1: Calculate the total moles of ions in each solution
To do this, we'll use the formula:
moles = concentration (M) x volume (L)
For the potassium iodide solution:
moles of KI = 0.203 M x 0.070 L = 0.01421 mol
For the ammonium sulfate solution:
moles of (NH4)2SO4 = 0.246 M x 0.035 L = 0.00861 mol
Step 2: Calculate the total moles of ions in the combined solution
Since potassium iodide dissociates into two ions (K+ and I-), and ammonium sulfate dissociates into three ions ((NH4)+ and (SO4)2-), we need to multiply the moles by their respective coefficients.
Total moles of ions in the combined solution:
moles of ions = 2 x moles of KI + 3 x moles of (NH4)2SO4
= 2 x 0.01421 mol + 3 x 0.00861 mol
= 0.05783 mol
Step 3: Calculate the total volume of the combined solution
To find the total volume of the combined solution, we'll add the volumes of the two solutions.
Total volume = volume of KI solution + volume of (NH4)2SO4 solution
= 70.0 mL + 35.0 mL
= 105.0 mL
Step 4: Convert the total volume to liters
Since the ionic strength is typically reported in units of mol/L or M (molarity), we need to convert the total volume to liters by dividing by 1000.
Total volume = 105.0 mL = 105.0 mL x (1 L/1000 mL) = 0.105 L
Step 5: Calculate the ionic strength
Finally, we can calculate the ionic strength using the formula:
Ionic strength (I) = (1/2) ∑ (c_i * z_i^2)
Where ∑ (c_i * z_i^2) is the sum of the product of the concentration (c_i) of each ion and its charge squared (z_i^2).
For our case, we have two ions with different charges, K+ with a charge of +1 and I- with a charge of -1. Thus, K+ contributes 1 mole of positive charge and I- contributes 1 mole of negative charge.
Ionic strength (I) = (1/2) * [ c(K+) * z(K+)^2 + c(I-) * z(I-)^2 ]
= (1/2) * [ c(K+) * (1)^2 + c(I-) * (-1)^2 ]
= (1/2) * [ c(K+) + c(I-) ]
= (1/2) * [ moles of K+ / total volume + moles of I- / total volume ]
= (1/2) * [ 2 x 0.01421 mol / 0.105 L + 2 x 0.01421 mol / 0.105 L ]
≈ 0.241 M
Therefore, the ionic strength of the combined solution is approximately 0.241 M.