<u>Answer:</u>
<u>For a:</u> The activity coefficient of copper ions is 0.676
<u>For b:</u> The activity coefficient of potassium ions is 0.851
<u>For c:</u> The activity coefficient of potassium ions is 0.794
<u>Explanation:</u>
To calculate the activity coefficient of an ion, we use the equation given by Debye and Huckel, which is:
........(1)
where,
= activity coefficient of ion
= charge of the ion
= ionic strength of solution
= diameter of the ion in nm
To calculate the ionic strength, we use the equation:
......(2)
where,
= concentration of i-th ions
= charge of i-th ions
We are given:
0.01 M NaCl solution:
Calculating the ionic strength by using equation 2:

Putting values in equation 2, we get:
![\mu=\frac{1}{2}[(0.01\times (+1)^2)+(0.01\times (-1)^2)]\\\\\mu=0.01M](https://tex.z-dn.net/?f=%5Cmu%3D%5Cfrac%7B1%7D%7B2%7D%5B%280.01%5Ctimes%20%28%2B1%29%5E2%29%2B%280.01%5Ctimes%20%28-1%29%5E2%29%5D%5C%5C%5C%5C%5Cmu%3D0.01M)
Now, calculating the activity coefficient of
ion in the solution by using equation 1:

Putting values in equation 1, we get:

Hence, the activity coefficient of copper ions is 0.676
We are given:
0.025 M HCl solution:
Calculating the ionic strength by using equation 2:

Putting values in equation 2, we get:
![\mu=\frac{1}{2}[(0.025\times (+1)^2)+(0.025\times (-1)^2)]\\\\\mu=0.025M](https://tex.z-dn.net/?f=%5Cmu%3D%5Cfrac%7B1%7D%7B2%7D%5B%280.025%5Ctimes%20%28%2B1%29%5E2%29%2B%280.025%5Ctimes%20%28-1%29%5E2%29%5D%5C%5C%5C%5C%5Cmu%3D0.025M)
Now, calculating the activity coefficient of
ion in the solution by using equation 1:

Putting values in equation 1, we get:

Hence, the activity coefficient of potassium ions is 0.851
We are given:
0.02 M
solution:
Calculating the ionic strength by using equation 2:

Putting values in equation 2, we get:
![\mu=\frac{1}{2}[(0.04\times (+1)^2)+(0.02\times (-2)^2)]\\\\\mu=0.06M](https://tex.z-dn.net/?f=%5Cmu%3D%5Cfrac%7B1%7D%7B2%7D%5B%280.04%5Ctimes%20%28%2B1%29%5E2%29%2B%280.02%5Ctimes%20%28-2%29%5E2%29%5D%5C%5C%5C%5C%5Cmu%3D0.06M)
Now, calculating the activity coefficient of
ion in the solution by using equation 1:

Putting values in equation 1, we get:

Hence, the activity coefficient of potassium ions is 0.794