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Chapter 4: Problem 119

Silver nitrate is a very expensive chemical. For a particular experiment, you need \(100.0 \mathrm{mL}\) of \(0.0750 \mathrm{M}\) \(\mathrm{AgNO}_{3},\) but only \(60 \mathrm{mL}\) of \(0.0500 \mathrm{M} \mathrm{AgNO}_{3}\) is available. You decide to pipet exactly \(50.00 \mathrm{mL}\) of the solution into a \(100.0 \mathrm{mL}\) flask, add an appropriate mass of \(\mathrm{AgNO}_{3},\) and then dilute the resulting solution to exactly \(100.0 \mathrm{mL}\). What mass of \(\mathrm{AgNO}_{3}\) must you use?

Short Answer

Expert verified
You must use 0.849 g of \(AgNO_{3}\)

Step by step solution

01

Calculate moles needed for final solution

First, calculate the number of moles needed for the final solution using the equation \(M = n/v\), where \(M\) is the molarity, \(n\) is the number of moles, and \(v\) is the volume (in litres). The final solution has a volume of 0.100 litres (or 100.0 mL) and a molarity of 0.075 mol/L, so you need \(n = M*v = 0.075 \times 0.100 = 0.0075\) mol of \(AgNO_{3}\)
02

Calculate moles in initial solution

Next, calculate the number of moles in the initial solution (again using \(M = n/v\)), which has a volume of 0.050 L and a molarity of 0.050 mol/L. This gives \(n = M*v = 0.050 \times 0.050 = 0.0025\) mol of \(AgNO_{3}\)
03

Calculate moles of \(AgNO_{3}\) to be added

Now, subtract the number of moles in the initial solution from the number of moles needed for the final solution. This gives \(0.0075 - 0.0025 = 0.0050\) mol.
04

Calculate mass of \(AgNO_{3}\) to be added

Finally, convert the number of moles to be added into mass using the molar mass of \(AgNO_{3}\), which is 169.87 g/mol. This gives the mass as \(m = n \times mw = 0.0050 \times 169.87 = 0.849 g\).

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Most popular questions from this chapter

A drop \((0.05 \mathrm{mL})\) of \(12.0 \mathrm{M} \mathrm{HCl}\) is spread over a sheet of thin aluminum foil. Assume that all the acid reacts with, and thus dissolves through, the foil. What will be the area, in \(\mathrm{cm}^{2}\), of the cylindrical hole produced? (Density of \(\mathrm{Al}=2.70 \mathrm{g} / \mathrm{cm}^{3} ;\) foil thickness \(=0.10 \mathrm{mm} .)\) \(2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})\)

Consider the reaction below: \(2 \mathrm{AgNO}_{3}(\mathrm{aq})+\mathrm{Na}_{2} \mathrm{S}(\mathrm{aq}) \longrightarrow\) $$ \mathrm{Ag}_{2} \mathrm{S}(\mathrm{s})+2 \mathrm{NaNO}_{3}(\mathrm{aq}) $$ (a) How many grams of \(\mathrm{Na}_{2} \mathrm{S}(\mathrm{s})\) are required to react completely with \(27.8 \mathrm{mL}\) of \(0.163 \mathrm{M} \mathrm{AgNO}_{3} ?\) (b) How many grams of \(\mathrm{Ag}_{2} \mathrm{S}(\mathrm{s})\) are obtained from the reaction in part (a)?

Chromium(II) sulfate, \(\mathrm{CrSO}_{4^{\prime}}\) is a reagent that has been used in certain applications to help reduce carbon-carbon double bonds \((\mathrm{C}=\mathrm{C})\) in molecules to single bonds ( \(\mathrm{C}-\mathrm{C}\) ). The reagent can be prepared via the following reaction. $$\begin{array}{c} 4 \mathrm{Zn}(\mathrm{s})+\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \longrightarrow 4 \mathrm{ZnSO}_{4}(\mathrm{aq})+2 \mathrm{CrSO}_{4}(\mathrm{aq})+\mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \end{array}$$

Write chemical equations to represent the following reactions. (a) Calcium phosphate is heated with silicon dioxide and carbon, producing calcium silicate \(\left(\mathrm{CaSiO}_{3}\right)\) phosphorus ( \(\mathrm{P}_{4}\) ), and carbon monoxide. The phosphorus and chlorine react to form phosphorus trichloride, and the phosphorus trichloride and water react to form phosphorous acid. (b) Copper metal reacts with gaseous oxygen, carbon dioxide, and water to form green basic copper carbonate, \(\mathrm{Cu}_{2}(\mathrm{OH})_{2} \mathrm{CO}_{3}\) (a reaction responsible for the formation of the green patina, or coating, often seen on outdoor bronze statues). (c) White phosphorus and oxygen gas react to form tetraphosphorus decoxide. The tetraphosphorus decoxide reacts with water to form an aqueous solution of phosphoric acid. (d) Calcium dihydrogen phosphate reacts with sodium hydrogen carbonate (bicarbonate), producing calcium phosphate, sodium hydrogen phosphate, carbon dioxide, and water (the principal reaction occurring when ordinary baking powder is added to cakes, bread, and biscuits).

A \(25.00 \mathrm{mL}\) sample of \(\mathrm{HCl}(\mathrm{aq})\) was added to a \(0.1000 \mathrm{g}\) sample of \(\mathrm{CaCO}_{3}\). All the \(\mathrm{CaCO}_{3}\) reacted, leaving some excess HCl(aq). \(\mathrm{CaCO}_{3}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \longrightarrow\) $$ \mathrm{CaCl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{CO}_{2}(\mathrm{g}) $$ The excess HCl(aq) required 43.82 mL of 0.01185 M \(\mathrm{Ba}(\mathrm{OH})_{2}\) to complete the following reaction. What was the molarity of the original HCl(aq)? $$2 \mathrm{HCl}(\mathrm{aq})+\mathrm{Ba}(\mathrm{OH})_{2}(\mathrm{aq}) \longrightarrow \mathrm{BaCl}_{2}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$$
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