A scientist wants to make a solution of tribasic sodium phosphate, \rm Na_3PO_4, for a laboratory experiment. How many grams of \rm Na_3PO_4 will be needed to produce 250 mL of a solution that has a concentration of \rm Na^+ ions of 0.600 \it M?
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To determine how many grams of tribasic sodium phosphate (Na₃PO₄) are needed to make a solution with a given concentration of Na⁺ ions, we can follow these steps:
Step 1: Determine the molar mass of Na₃PO₄
The molar mass of Na₃PO₄ can be calculated by summing the atomic masses of each element:
Na: 22.99 g/mol
P: 30.97 g/mol
O: 16.00 g/mol (three oxygens in Na₃PO₄)
Molar mass of Na₃PO₄ = (3 * Na) + P + (4 * O) = (3 * 22.99 g/mol) + 30.97 g/mol + (4 * 16.00 g/mol)
Step 2: Calculate the number of moles of Na⁺ ions
The concentration of Na⁺ ions is given as 0.600 M, which means 0.600 moles of Na⁺ ions are present in 1 liter (1000 mL) of solution. Since we only want to make a 250 mL solution, we need to adjust the number of moles accordingly:
Number of moles of Na⁺ ions = 0.600 M * 0.250 L = 0.150 moles
Step 3: Convert moles to grams
To convert from moles to grams, we multiply the number of moles by the molar mass of Na₃PO₄. This will give us the mass of Na₃PO₄ required to produce the desired concentration of Na⁺ ions.
Mass of Na₃PO₄ = number of moles * molar mass
Now you can substitute the values into the equation and calculate the mass of Na₃PO₄ needed.