The phosphorus content in a dilute fertilizer solution was found to be 7.56 ug/m

Question

The phosphorus content in a dilute fertilizer solution was found to be 7.56 ug/mL with a standard error of 0.05 ?g/mL with a df=5. The dilute fertilizer solution was prepared as follows: 1.0922g fertilizer was dissolved in DI water to make a 1L solution, 5mL of the resulting solution is diluted to 100mL to make the dilute fertilizer solution. Calculate the standard error in the %P2O5 in the fertilizer. (assume there is no error in the molar masses, the dilution volumes, and the mass of the fertilizer) Standard Error = ________%

Explanation / Answer

Phosphorus content in dilute fertilizer, X = 7.56 ± 0.05 g/mL

Molecular weight of phosphorus = 30.974 g/mol

Molecular weight of P2O5 = 141.95 g/mol

P2O5 content in dilute fertilizer, Y = X * 141.95 / 30.974 * (100 mL)

= 3464.56 ± 22.91 g = 0.00346456 ± 2.29 x 10-5 g

Only 5 mL of fertilizer is used to make dilute fertilizer solution out of 1 L

Mass of fertilizer in dilute fertilizer solution, Z = 1.0922 * 5 /1000 = 0.00546 g

% P2O5 in the fertilizer = Y / Z * 100 = 63.44 ± 0.42 %

Standard error = 0.42 %

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