<u>Answer:</u> The mole fraction of KCl in the solution is 0.044
<u>Explanation:</u>
To calculate the number of moles, we use the equation:
.....(1)
Given mass of KCl = 43.0 g
Molar mass of KCl = 74.5 g/mol
Putting values in equation 1, we get:
![\text{Moles of KCl}=\frac{43g}{74.5g/mol}=0.58mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20KCl%7D%3D%5Cfrac%7B43g%7D%7B74.5g%2Fmol%7D%3D0.58mol)
Given mass of water = 225 g
Molar mass of water = 18 g/mol
Putting values in equation 1, we get:
![\text{Moles of water}=\frac{225g}{18g/mol}=12.5mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20water%7D%3D%5Cfrac%7B225g%7D%7B18g%2Fmol%7D%3D12.5mol)
To calculate the mole fraction of a substance, we use the equation:
![\chi_A=\frac{n_A}{n_A+n_B}](https://tex.z-dn.net/?f=%5Cchi_A%3D%5Cfrac%7Bn_A%7D%7Bn_A%2Bn_B%7D)
Moles of KCl = 0.58 moles
Moles of water = 12.5 moles
Putting values in above equation:
![\chi_{KCl}=\frac{n_{KCl}}{n_{KCl}+n_{\text{water}}}](https://tex.z-dn.net/?f=%5Cchi_%7BKCl%7D%3D%5Cfrac%7Bn_%7BKCl%7D%7D%7Bn_%7BKCl%7D%2Bn_%7B%5Ctext%7Bwater%7D%7D%7D)
![\chi_{KCl}=\frac{0.58}{0.58+12.5}\\\\\chi_{KCl}=0.044](https://tex.z-dn.net/?f=%5Cchi_%7BKCl%7D%3D%5Cfrac%7B0.58%7D%7B0.58%2B12.5%7D%5C%5C%5C%5C%5Cchi_%7BKCl%7D%3D0.044)
Hence, the mole fraction of KCl in the solution is 0.044