To determine the final concentration of phosphate anion in both ppm and molarity, we will follow these steps:
- Calculate the amount of phosphate from the 0.5 M orthophosphate solution.
- Calculate the amount of phosphate from the 5000 ppm orthophosphate solution.
- Add both amounts together to find the total amount of phosphate.
- Calculate the final concentration in molarity.
- Calculate the final concentration in ppm.
Step 1: Calculate the amount of phosphate from the 0.5 M orthophosphate solution.
- Volume of orthophosphate solution = 50 mL = 0.050 L
- Molarity (M) of the solution = 0.5 M
\[ \text{Moles of phosphate from 0.5 M solution} = \text{Volume (L)} \times \text{Molarity (mol/L)} = 0.050 , L \times 0.5 , \text{mol/L} = 0.025 , \text{mol} \]
Step 2: Calculate the amount of phosphate from the 5000 ppm orthophosphate solution.
- The concentration of the solution is 5000 ppm, which is equivalent to 5000 mg/L.
- To convert this to molarity, we need the molar mass of phosphate (PO₄³⁻). The molar mass of PO₄³⁻ is approximately 94.97 g/mol.
First, convert 5000 mg to grams: \[ 5000 , \text{mg} = 5 , \text{g} \]
Now, convert grams to moles: \[ \text{Moles of phosphate} = \frac{\text{grams}}{\text{molar mass}} = \frac{5 , \text{g}}{94.97 , \text{g/mol}} \approx 0.0527 , \text{mol} \]
Step 3: Total moles of phosphate
Total moles of phosphate: \[ \text{Total moles} = 0.025 , \text{mol} + 0.0527 , \text{mol} \approx 0.0777 , \text{mol} \]
Step 4: Calculate the final molarity
The final total volume of the solution = 250 mL = 0.250 L.
Now, calculate the molarity: \[ \text{Final Molarity (M)} = \frac{\text{Total moles}}{\text{Total volume (L)}} = \frac{0.0777 , \text{mol}}{0.250 , L} \approx 0.3108 , \text{M} \]
Step 5: Calculate the final concentration in ppm
1 mole of phosphate weighs approximately 94.97 grams.
To find the concentration in ppm:
- Convert moles to grams: \[ \text{grams of phosphate} = 0.0777 , \text{mol} \times 94.97 , \text{g/mol} \approx 7.386 , \text{g} \]
- Now, convert grams to mg: \[ 7.386 , \text{g} = 7386 , \text{mg} \]
Now, since we have a total volume of 250 mL, the concentration in ppm is: \[ \text{ppm} = \frac{\text{mg of solute}}{\text{L of solution}} = \frac{7386 , \text{mg}}{0.250 , \text{L}} = 29544 , \text{ppm} \]
Final Results
- Concentration in molarity: \(0.3107692 , \text{M} \approx 0.310769 , \text{M} \) (to 7 significant figures)
- Concentration in ppm: \(29544 , \text{ppm} \) (to 4 significant figures)
Therefore, the final concentrations are:
- Molarity: \(0.310769 , \text{M}\)
- Concentration: \(29544 , \text{ppm}\)