Problem 49 - General Chemistry: Principles and Modern Applications

Question

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)?

Step-by-Step Solution

Answer

(a) The mass of Na2S required to react completely is 0.1766 grams. (b) The mass of Ag2S obtained from the reaction is 0.5604 grams.

Step 1: Calculation of Moles of AgNO3

The moles of AgNO3 can be calculated using the formula:Moles = Molarity (M) × Volume (L)Given Molarity = 0.163M and Volume = 27.8 mL = 0.0278 LMoles = 0.163 × 0.0278 = 0.004526 moles

Step 2: Find the Moles of Na2S

From the balanced chemical equation, the stoichiometric ratio of AgNO3 to Na2S is 2:1. Thus, the number of moles of Na2S that will react with AgNO3 is: Moles of Na2S = Moles of AgNO3 / 2 = 0.004526 /2 = 0.002263 moles

Step 3: Find the Mass of Na2S Required

The molar mass of Na2S (sodium sulfide) is 78.045 g/mol. The mass of sodium sulfide (Na2S) can be calculated using the following formula:Mass (g) = Moles × Molar mass Mass (g) = 0.002263 moles × 78.045 g/mole = 0.1766 grams

Step 4: Find the moles of Ag2S Produced

From the balanced chemical equation, the stoichiometric ratio of AgNO3 to Ag2S is 2:1. Thus, the number of moles of Ag2S produced is : Moles of Ag2S = Moles of AgNO3 / 2 = 0.004526 /2 = 0.002263 moles

Step 5: Find the Mass of Ag2S Produced

The molar mass of Ag2S (silver sulfide) is 247.8 g/mol.The mass (g) of silver sulfide (Ag2S) can be calculated using the same formula as indicated previously: Mass (g) = Moles × Molar mass Mass (g) = 0.002263 moles × 247.8 g/mole = 0.5604 grams

Key Concepts

Understanding Chemical Reactions

A chemical reaction is a process where reactants are transformed into products. In the provided reaction, we have sodium sulfide \((\mathrm{Na}_2 \mathrm{S})\) and silver nitrate \((\mathrm{AgNO}_3)\) as reactants. They react to form silver sulfide \((\mathrm{Ag}_2 \mathrm{S})\) and sodium nitrate \((\mathrm{NaNO}_3)\).
During such reactions:

• Bonds between atoms in the reactants break.
• New bonds form to create the products.

Stoichiometry helps us understand the proportions in which substances react, ensuring there is neither excess nor shortage of any reactant. In our example, according to the balanced chemical equation, two moles of \(\mathrm{AgNO}_3\) are needed to react with one mole of \(\mathrm{Na}_2 \mathrm{S}\) to produce one mole of \(\mathrm{Ag}_2 \mathrm{S}\). This ratio is crucial when calculating reactants and products. Ensuring the correct stoichiometric ratio is like having your recipe's ingredients in the right proportions to get delicious food!

Exploring Molarity

Molarity is a measure of the concentration of a solution. It indicates how much of a substance is dissolved in a given volume of solution. It is expressed in moles per liter \((\mathrm{mol/L})\).
To find out how many moles of \(\mathrm{AgNO}_3\) we have, we use the formula: \[\text{Moles of } \mathrm{AgNO}_3 = \text{Molarity} \times \text{Volume}\]where the volume needs to be in liters. In this case, the \(\mathrm{AgNO}_3\) solution has a molarity of 0.163 M, and we deal with a volume of 27.8 mL, which is equivalent to 0.0278 L. Plugging these into the formula gives us the moles available for the reaction.
Understanding molarity helps in determining how concentrated a solution is, which in turn influences the reaction's outcome. Higher molarity implies more reactants are available, increasing reaction efficiency if handled correctly. Therefore, calculating molarity accurately is key to predicting how effectively reactants will transform into products.

Steps in Mass Calculation

Mass calculation in stoichiometry tells us the quantity of reactants needed and the amount of product expected. Let's break it down:
**Converting Moles to Mass** Once we determine the moles of a substance, we use its molar mass to find the mass. This is done using the formula: \[\text{Mass} = \text{Moles} \times \text{Molar Mass}\]For instance, using \(\mathrm{Na}_2 \mathrm{S}\), we have calculated 0.002263 moles using stoichiometry. Given its molar mass is 78.045 g/mol, the formula helps determine the grams needed. It’s crucial to ensure the unit conversion is correct and the molecular weight is accurate to get precise results.
**Example for Products** The same principle applies to calculating the mass of products, like \(\mathrm{Ag}_2 \mathrm{S}\). After determining its moles from the reaction, multiply by its molar mass (247.8 g/mol) to find the corresponding mass. Accurate mass calculations help predict precise amounts of substances needed or generated, avoiding wastage and ensuring process efficiency.