What mass of solid AgBr is produced when 100.0 \(\mathrm{mL}\) of 0.150 \(\mathrm{MAgNO}_{3}\) is added to 20.0 \(\mathrm{mL}\) of 1.00 $\mathrm{M} \mathrm{NaBr} ?$

Short Answer

Expert verified
The mass of solid AgBr produced when 100.0 mL of 0.150 M AgNO3 is added to 20.0 mL of 1.00 M NaBr is approximately 2.82 g.

Step by step solution

01

Write the balanced chemical equation

First, we need to write the balanced chemical equation for the reaction between AgNO3 and NaBr to obtain AgBr and NaNO3. The balanced chemical equation is as follows: \[AgNO_{3}(aq) + NaBr(aq) \rightarrow AgBr(s) + NaNO_{3}(aq)\]
02

Find moles of each reactant

To find the limiting reactant, we must first determine the moles of each reactant present in the reaction. We will use the given volumes and concentrations to calculate the number of moles for each reactant. For AgNO3: Moles = (volume in L) × (concentration in M) Moles of AgNO3 = (100.0 mL × (1 L/1000 mL)) × (0.150 mol/L) Moles of AgNO3 = 0.015 mol For NaBr: Moles = (volume in L) × (concentration in M) Moles of NaBr = (20.0 mL × (1 L/1000 mL)) × (1.00 mol/L) Moles of NaBr = 0.020 mol
03

Identify the limiting reactant

Now, we will compare the moles of reactants to determine the limiting reactant. The stoichiometry of the balanced chemical equation shows us that 1 mole of AgNO3 reacts with 1 mole of NaBr. From the calculated moles of reactants: 0.015 mol AgNO3 × (1 mol NaBr / 1 mol AgNO3) = 0.015 mol NaBr Since we have 0.020 mol of NaBr, but only 0.015 mol are required to react with the available AgNO3, AgNO3 is the limiting reactant. The reaction will stop when all 0.015 mol of AgNO3 have been consumed.
04

Calculate the mass of AgBr produced

Since AgNO3 is the limiting reactant, the amount of AgBr produced will depend on the moles of AgNO3. We will use the stoichiometry of the balanced chemical equation to find the moles of AgBr produced. Moles of AgBr produced = (moles of limiting reactant AgNO3) × (1 mol AgBr / 1 mol AgNO3) Moles of AgBr produced = 0.015 mol Now, we will convert moles of AgBr to mass. To do this, we need to know the molar mass of AgBr, which is approximately 187.77 g/mol. Mass of AgBr = (moles of AgBr) × (molar mass of AgBr) Mass of AgBr = (0.015 mol) × (187.77 g/mol) Mass of AgBr = 2.82 g The mass of solid AgBr produced is approximately 2.82 g.

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