Question

A sample of 30.00 grams of potassium phosphate was added to a solution containing 100.0 mL of 0.25 M calcium nitrate. Calcium phosphate was precipitated according to the following reaction. 2K3PO4(s) + 3Ca(NO3)2(aq) - Ca3(PO4)2(s) + 6KNO3(aq) 2.25 grams of Calcium phosphate were recovered. Calculate the theoretical yield and the percent yield.​

Answer 1

Theoretical yield of Ca₃(PO₄)₂ = 19.67 g

Percent yield of Ca₃(PO₄)₂ = 11.4 %

Step-by-step explanation:

Data given

Potassium Phosphate K₃PO₄ = 30.00 g

calcium nitrate Ca(NO₃)₂ of 0.25 M = 100.0 mL

Reaction given:

2K₃PO₄(s) + 3Ca(NO₃)₂(aq) ---------> Ca₃(PO₄)₂(s) + 6KNO₃(aq)

Solution :

Part A :

To find the theoretical yield of Calcium phosphate

Look at the reaction :

2K₃PO₄(s) + 3Ca(NO₃)₂(aq) ---------> Ca₃(PO₄)₂(s) + 6KNO₃(aq)

2 mol 3 mol 1 mol 6mol

So,

2 mol of 2K₃PO₄ give 1 mole of Ca₃(PO₄)₂

if we represent mole in mass then

Molar Mass of K₃PO₄ = 3(39) + 31 + 4(16)

Molar Mass of K₃PO₄ = 212 g/mol

and

Molar mass of Ca₃(PO₄)₂ = [ 3(40) + 2((31) + 4(16))]

Molar mass of Ca₃(PO₄)₂ = [ 120 + 62 + 96] = 278 g/mol

Molar mass of Ca₃(PO₄)₂ = 278 g/mol

Now, if we write it in grams

2K₃PO₄(s) + 3Ca(NO₃)₂(aq) ---------> Ca₃(PO₄)₂(s) + 6KNO₃(aq)

2 mol 3 mol 1 mol 6mol

2 mol ( 212 g/mol) 1 mol (278 g/mol)

424 g 278 g

So from the above information we come to know that

424 g of K₃PO₄ gives 278 g of Ca₃(PO₄)₂

then 30 g will give how much Ca₃(PO₄)₂ Calcium phosphate

Apply unity formula

424 g of K₃PO₄ ≅ 278 g of Ca₃(PO₄)₂

30 g of K₃PO₄ ≅ x g of Ca₃(PO₄)₂

By doing cross multiplication and rearranging the above values

x g of Ca₃(PO₄)₂ = 278 g x 30 g / 424 g

x g of Ca₃(PO₄)₂ = 19.67 g

So,

30 g of K₃PO₄ will give 19.67 g Ca₃(PO₄)₂ theoretically.

Theoretical yield of Ca₃(PO₄)₂ = 19.67 g

Now,

Part B :

To find percent yield of Ca₃(PO₄)₂

Solution

Data given:

Actual yield of Ca₃(PO₄)₂ = 2.25 g

Theoretical yield of Ca₃(PO₄)₂ = 19.67 g

Formula to be used:

Percentage yield = Actual yield/ theoretical yield x 100 %

Put values in Above formula

Percent yield = 2.25 g / 19.67 g x 100 %

Percent yield = 0.1144 / 100 %

Percent yield = 11.4 %

So,

Percent yield of Ca₃(PO₄)₂ = 11.4 %