Question

Consider the reaction between silver and nitric acid for which the equation is \(\mathrm{Ag}(s)+2 \mathrm{H}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow{\mathrm{Ag}^{+}(a q)+\mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}}\) If \(42.50 \mathrm{~mL}\) of \(12.0 \mathrm{M}\) nitric acid furnishes enough \(\mathrm{H}^{+}\) to react with silver, how many grams of silver react?

Short answer

Answer: 27.5 g of silver will react with the given amount of nitric acid.

Step-by-step solution

Calculate the moles of \(\mathrm{H}^{+}\)

First, we will calculate the number of moles of \(\mathrm{H}^{+}\) ions present in \(42.50 \mathrm{~mL}\) of \(12.0 \mathrm{M}\) nitric acid. To do this, we will convert the volume in milliliters (mL) to liters (L) and use the molarity of nitric acid: Moles of \(\mathrm{H}^{+} = 12.0 \mathrm{M} \times 42.50 \mathrm{~mL} \times \dfrac{1 \mathrm{~L}}{1000 \mathrm{~mL}}\) Moles of \(\mathrm{H}^{+} = 12.0 \times 42.50 \times \dfrac{1}{1000} = 0.51 \ \mathrm{mol}\) of \(\mathrm{H}^{+}\)

Determine the moles of silver

Now, let's use the stoichiometry of the balanced reaction to determine the moles of silver that react with the calculated moles of \(\mathrm{H}^{+}\): \(\dfrac{1 \mathrm{~mol}\ Ag}{2 \mathrm{~mol}\ H^{+}}=\dfrac{n(\mathrm{Ag})}{0.51\ \mathrm{mol}\ H^{+}}\) Here, \(n(\mathrm{Ag})\) represents the moles of silver. Solve for the moles of silver: \(n(\mathrm{Ag})=\dfrac{1 \mathrm{~mol}\ Ag}{2 \mathrm{~mol}\ H^{+}} \times 0.51\ \mathrm{mol}\ H^{+} = 0.255 \ \mathrm{mol}\ Ag\)

Calculate the mass of silver

Lastly, we will use the molar mass of silver, \(M(\mathrm{Ag}) = 107.87 \mathrm{~g/mol}\), to convert the number of moles to grams: Mass of silver = \(0.255 \ \mathrm{mol}\ Ag \times \dfrac{107.87 \mathrm{~g}}{1 \mathrm{~mol}\ Ag} = 27.5 \mathrm{~g}\). Thus, \(27.5 \mathrm{~g}\) of silver will react with the given amount of nitric acid.

Key concepts

Chemical Reactions

Understanding chemical reactions is crucial for solving stoichiometry problems. A chemical reaction involves the transformation of reactants into products through the breaking and forming of chemical bonds. Let's break down the provided example. The equation given is a representation of the reaction between silver (Ag) and nitric acid (HNO3), where Ag acts as a reactant with the hydrogen ions (H+) and nitrate ions (NO3-) from the acid to produce silver ions (Ag+), nitrogen dioxide (NO2), and water (H2O).

When working with chemical reactions, it's important to ensure the equation is balanced, which means the number of atoms for each element is the same on both sides of the equation. This allows us to use the coefficients to determine the stoichiometric relationships between reactants and products, which is pivotal in finding how many grams of silver react, as demonstrated in the exercise. These coefficients become the bridge in the 'mole ratio,' fundamental to solving the problem.

Molarity Calculations

Molarity is a measurement of concentration in chemistry, specifically the number of moles of a substance per liter of solution. Molarity calculations are an integral part of stoichiometry problems, as they allow us to convert between the volume of a solution and the moles of solute contained within it. In the example problem, we're given a 12.0 M solution of nitric acid. The 'M' stands for molarity, which translates to 12.0 moles of solute in every liter of solution.

To find how many moles of H+ from nitric acid react, we need to use the volume of the nitric acid solution provided (42.50 mL) and its molarity. By converting the volume to liters and multiplying by the molarity, we calculate the moles of H+ available to react with silver. This particular calculation is the initial step in linking the volume of a solution to the mass of a reactant or product in a chemical reaction.

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a bridge between the atomic world and the macroscopic world we can measure. One mole is defined as exactly 6.02214076×10²³ elementary entities (this number is known as Avogadro's number) and is the amount of substance that contains as many particles as there are atoms in 12 g of carbon-12.

In stoichiometry, the mole concept allows us to translate between the mass of a substance and the amount in terms of moles. Using the molar mass of silver (107.87 g/mol), which is the mass of one mole of silver atoms, we can convert moles of silver to mass. This final step provides the answer to the initial query: the mass of silver that will react with a given volume of nitric acid solution. It is by understanding and applying the mole concept that such conversions become possible, and they're essential to performing stoichiometric calculations in a variety of chemical contexts.