Calculate the ionic strength of a solution that contains 1.45g Na3PO4 in 0.500L of solution.
To calculate the ionic strength of a solution, we need to first determine the concentration of each ion present in the solution and then apply the appropriate formula.
In this case, we have Na3PO4, which dissociates into 3 Na+ ions and 1 PO4^3- ion in solution.
Let's calculate the molar concentration of Na3PO4 by converting the given mass (1.45g) to moles and dividing by the volume of the solution (0.500L):
Molar mass of Na3PO4 = (3 * molar mass of Na) + molar mass of P + (4 * molar mass of O)
= (3 * 22.99 g/mol) + 30.97 g/mol + (4 * 16.00 g/mol)
= 163.94 g/mol
Number of moles of Na3PO4 = mass / molar mass
= 1.45 g / 163.94 g/mol
= 0.00885 mol
Molar concentration of Na3PO4 = moles / volume
= 0.00885 mol / 0.500 L
= 0.0177 mol/L
Now, let's calculate the molar concentration of each ion. Since we have 3 Na+ ions, the concentration of Na+ will be 3 times that of Na3PO4:
Molar concentration of Na+ = 3 * molar concentration of Na3PO4
= 3 * 0.0177 mol/L
= 0.0531 mol/L
Similarly, the concentration of PO4^3- will be the same as that of Na3PO4:
Molar concentration of PO4^3- = molar concentration of Na3PO4
= 0.0177 mol/L
Finally, we can calculate the ionic strength using the formula:
Ionic strength (I) = (1/2) * (sum of cation concentration * charge^2)
= (1/2) * [(concentration of Na+ * charge of Na+)^2 + (concentration of PO4^3- * charge of PO4^3-)^2]
= (1/2) * [(0.0531 mol/L * 1)^2 + (0.0177 mol/L * -3)^2]
= (1/2) * [(0.0531)^2 + (0.0177 * -3)^2]
= (1/2) * [0.002812 + 0.001764]
= (1/2) * 0.004576
= 0.002288
Therefore, the ionic strength of the solution is 0.002288.