Question

2021 ap chemistry free-response questions

1. a student is given the task of determining the molar concentration of a cuso₄ solution using two different procedures, precipitation and spectrophotometry.

for the precipitation experiment, the student adds 20.0 ml of 0.200 m ba(no₃)₂ to 50.0 ml of the cuso₄(aq). the reaction goes to completion, and a white precipitate forms. the student filters the precipitate and dries it overnight. the data are given in the following table.
mass of dry filter paper: 0.764 g
volume of cuso₄(aq): 50.0 ml
volume of 0.200 m ba(no₃)₂: 20.0 ml
mass of filter paper and dried precipitate: 1.136 g
(a) write a balanced net ionic equation for the precipitation reaction.
(b) calculate the number of moles of precipitate formed.
(c) calculate the molarity of the original cuso₄ solution.
for the spectrophotometry experiment, the student first makes a standard curve. the student uses a 0.1000 m solution of cuso₄(aq) to make three more solutions of known concentration (0.0500 m, 0.0300 m, and 0.0100 m) in 50.00 ml volumetric flasks.
(d) calculate the volume of 0.1000 m cuso₄(aq) needed to make 50.00 ml of 0.0500 m cuso₄(aq).

Explanation:

(a)

In a precipitation reaction between \(Ba(NO_3)_2\) and \(CuSO_4\), the relevant ions are \(Ba^{2+}\) and \(SO_4^{2 -}\). The net - ionic equation focuses on the ions that form the precipitate (\(BaSO_4\)). Spectator ions (\(Cu^{2+}\) and \(NO_3^{-}\)) are excluded.

Step1: Find the mass of the precipitate

The mass of the precipitate (\(m\)) is the mass of the filter paper and precipitate minus the mass of the filter paper.
\(m = 1.136\ g-0.764\ g=0.372\ g\)

Step2: Calculate the molar mass of \(BaSO_4\)

The molar mass of \(BaSO_4\): \(M=(137.3 + 32.07+4\times16.00)\ g/mol = 233.4\ g/mol\)

Step3: Calculate the moles of \(BaSO_4\)

Using the formula \(n=\frac{m}{M}\), where \(n\) is the number of moles, \(m\) is the mass, and \(M\) is the molar mass.
\(n=\frac{0.372\ g}{233.4\ g/mol}\approx0.00159\ mol\)

Step1: Use the mole - ratio from the balanced equation

From the balanced net - ionic equation \(Ba^{2+}(aq)+SO_4^{2 -}(aq)=BaSO_4(s)\), the mole ratio of \(SO_4^{2 -}\) (from \(CuSO_4\)) to \(BaSO_4\) is \(1:1\). So, \(n(CuSO_4)=n(BaSO_4) = 0.00159\ mol\)

Step2: Calculate the molarity of \(CuSO_4\)

The formula for molarity \(M=\frac{n}{V}\), where \(V = 50.0\ mL=0.0500\ L\)
\(M=\frac{0.00159\ mol}{0.0500\ L}=0.0318\ M\)

Answer:

\(Ba^{2+}(aq)+SO_4^{2 -}(aq)=BaSO_4(s)\)

(b)