Question

The label on a bottle of "organic" liquid fertilizer concentrate states that it contains 7.40 grams of phosphate per 100.0 mL and that 16.0 fluid ounces should be diluted with water to make 32.0 gallons of fertilizer to be applied to growing plants. What version of the dilution equation can be used to calculate the final phosphate concentration? Express your answer in terms of Vi, Ci, and Vf.

Answer 1

C = 7.4 g of PO4- / 100 mL

V = 16 oz fl. -- V = 32 gallon

Apply

We need to apply dilution law, which is based on the mass conservation principle

initial mass = final mass

this apply for moles as weel ( if there is no reaction, which is the case )

mol of A initially = mol of A finally

or, for this case

moles of A in stock = moles of A in diluted solution

Recall that

mol of A = Molarity of A * Volume of A

then

moles of A in stock = moles of A in diluted solution

Molarity of A in stock * Volume of A in stock = Molarity of A in diluted solution* Volume of A in diluted solution

Now, substitute known data

C1 = 7.4 g / 100 mL = 0.074 g/mL

Vinitial = 16 fl oz = 473.176 mL

Cfinal =

Vfinal = 32 gal = 121.133 L = 121133 mL

now..

Cfinal = Cinitial * Vinitial / Vfinal = 0.074 g/mL * 473.176 mL / 121133 mL

Cfinal = 0.000289 g/mL