# 60.0 mL of 0.45 M #K_3PO_4# is mixed with 240.0 mL of 0.20 M #K_2SO_3#. What is the final concentration of all three ions in the solution?

The dissociation of the two salts—which are both soluble in aqueous solution—to produce negatively charged anions and positively charged cations is the key to solving this problem.

This indicates that the target solution's three ions will be

Two pieces of information are necessary in order to calculate the concentration of each ion in the finished solution.

Given the volume and molarities of the two solutions, you can calculate the number of moles of each salt you're mixing by using the definition of molarity, which is the number of moles of solute per liter of solution.

additionally

Find out how many moles of each ion are created in solution when the salts dissolve by examining the two balanced chemical equations.

As you can see, both salts are contributing potassium cations to the final solution, so you will have

The finished solution's overall volume will be

Consequently, in the finished solution, each ion's concentration will be

Two sig figs are used to round the answers.

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The final concentration of all three ions in the solution would be as follows:

- For K⁺ ions: (0.45 , \text{M} \times \left(\frac{60.0}{300.0}\right) + 0.20 , \text{M} \times \left(\frac{240.0}{300.0}\right))
- For PO₄³⁻ ions: (0.45 , \text{M} \times \left(\frac{60.0}{300.0}\right))
- For SO₃²⁻ ions: (0.20 , \text{M} \times \left(\frac{240.0}{300.0}\right))

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To find the final concentration of all three ions in the solution, you need to first calculate the moles of each ion present in the initial solutions, then add them up to find the total moles of each ion in the final solution. Finally, divide the total moles by the total volume of the final solution to find the final concentration of each ion.

For K3PO4: Initial moles = volume (L) × concentration (mol/L) Initial moles of K3PO4 = 0.060 L × 0.45 mol/L = 0.027 moles

For K2SO3: Initial moles = volume (L) × concentration (mol/L) Initial moles of K2SO3 = 0.240 L × 0.20 mol/L = 0.048 moles

Total moles of K ions in the final solution: Total moles of K ions = moles of K3PO4 + moles of K2SO3 Total moles of K ions = 0.027 moles + 2 × 0.048 moles = 0.123 moles

Total moles of P ions in the final solution: Total moles of P ions = moles of K3PO4 Total moles of P ions = 0.027 moles

Total moles of SO3 ions in the final solution: Total moles of SO3 ions = moles of K2SO3 Total moles of SO3 ions = 2 × 0.048 moles = 0.096 moles

Final concentration of K ions: Final concentration of K ions = Total moles of K ions / Total volume of solution Final concentration of K ions = 0.123 moles / (0.060 L + 0.240 L) = 0.307 M

Final concentration of P ions: Final concentration of P ions = Total moles of P ions / Total volume of solution Final concentration of P ions = 0.027 moles / (0.060 L + 0.240 L) = 0.0675 M

Final concentration of SO3 ions: Final concentration of SO3 ions = Total moles of SO3 ions / Total volume of solution Final concentration of SO3 ions = 0.096 moles / (0.060 L + 0.240 L) = 0.24 M

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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