Problem 34 - Chemistry: An Atoms-Focused Approach

Question

Pigments for Stoplights Cadmium yellow (cadmium sulfide) is a lemon-yellow pigment used in the lenses of stoplights. Its formula is CdS, and it is very insoluble in water. The recommended recipe for cadmium yellow is to mix cadmium nitrate with sodium sulfide in water. The cadmium yellow forms as a solid, while the other product, sodium nitrate, remains dissolved in the water. a. Write a balanced chemical equation for the reaction. b. Calculate the mass of cadmium nitrate you must start with to make 125 g of CdS.

Step-by-Step Solution

Answer

Answer: 266.78 g of cadmium nitrate is needed to produce 125 g of cadmium sulfide.

Step 1: Write the balanced chemical equation

First, we will write the balanced chemical equation for the reaction. We are given the reactants: cadmium nitrate (Cd(NO3)_2) and sodium sulfide (Na_2S). As stated in the problem, the products are cadmium sulfide (CdS) and sodium nitrate (NaNO3). Now, we can write the unbalanced chemical equation: Cd(NO3)_2 + Na_2S -> CdS + NaNO3 We need to balance the equation by ensuring equal numbers of each type of atom on both sides of the equation. Cd(NO3)_2 + 2 Na_2S -> CdS + 2 NaNO3 Now, the equation is balanced.

Step 2: Use stoichiometry to find the mass of cadmium nitrate needed

We are given that we want to produce 125 g of cadmium sulfide (CdS). To find the mass of cadmium nitrate (Cd(NO3)_2) needed, we will use stoichiometry. 1. Convert the mass of cadmium sulfide to moles using its molar mass. Molar mass of CdS = (112.41 g/mol for Cd) + (32.07 g/mol for S) = 144.48 g/mol Moles of CdS = (125 g CdS) / (144.48 g/mol) = 0.865 moles 2. Determine the mole ratio between cadmium nitrate and cadmium sulfide from the balanced equation. From the balanced equation, the mole ratio is 1:1. 3. Calculate the moles of cadmium nitrate needed. Since the mole ratio is 1:1, moles of Cd(NO3)_2 = moles of CdS = 0.865 moles 4. Convert the moles of cadmium nitrate to mass using its molar mass. Molar mass of Cd(NO3)_2 = (112.41 g/mol for Cd) + (2 * (14.01 g/mol for N)) + (6 * (16.00 g/mol for O)) = 308.42 g/mol Mass of Cd(NO3)_2 = (0.865 moles) * (308.42 g/mol) = 266.78 g Therefore, you must start with 266.78 g of cadmium nitrate to make 125 g of cadmium sulfide.

Key Concepts

Balanced Chemical Equation

When a chemical reaction occurs, a balanced chemical equation helps represent the conservation of mass. This means that the number of atoms of each element involved must be the same on both the reactant and product sides of the equation. Let's look at the reaction between cadmium nitrate and sodium sulfide to understand this better. We start with the unbalanced equation:\[ \text{Cd(NO}_3\text{)}_2 + \text{Na}_2\text{S} \rightarrow \text{CdS} + \text{NaNO}_3 \]Notice that the nitrate (NO₃) and sodium (Na) ions are not balanced. To achieve balance, we add coefficients to these compounds to satisfy the law of conservation of mass:\[ \text{Cd(NO}_3\text{)}_2 + 2\text{Na}_2\text{S} \rightarrow \text{CdS} + 2\text{NaNO}_3 \]Now, the equation is balanced, meaning equal quantities of each element are present on both sides. Understanding balanced chemical equations is crucial as it helps us figure out the proportions of reactants needed for a reaction, which is foundational in stoichiometry.

Molar Mass Calculation

Calculating molar mass is a key step in stoichiometry to determine the amount of a substance involved in a reaction. Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol).To find the molar mass of a compound, sum up the atomic masses of all the elements in its chemical formula. For instance, to find the molar mass of cadmium sulfide (CdS), we calculate as follows:

• Atomic mass of cadmium (Cd) is 112.41 g/mol
• Atomic mass of sulfur (S) is 32.07 g/mol

Thus, the molar mass of CdS:\[ 112.41 \text{ g/mol} + 32.07 \text{ g/mol} = 144.48 \text{ g/mol} \]Similarly, the molar mass of cadmium nitrate \((\text{Cd(NO}_3\text{)}_2)\) can be calculated by adding the molar masses of cadmium, nitrogen, and oxygen. This calculation is essential as it enables us to convert between grams and moles, facilitating the calculation of needed reactants or produced products.

Chemical Reaction

A chemical reaction involves the transformation of reactants into products through the breaking and forming of chemical bonds. In the context of manufacturing cadmium yellow, the reaction can be expressed as a transformation of cadmium nitrate and sodium sulfide to generate cadmium sulfide and sodium nitrate.Understanding chemical reactions involves comprehending the type of reactions and the process of rearranging atoms to produce new compounds. Here’s what happens:

• Reactants: Cadmium nitrate \((\text{Cd(NO}_3\text{)}_2)\) and sodium sulfide \((\text{Na}_2\text{S})\)
• Products: Cadmium sulfide \((\text{CdS})\) – a lemon-yellow pigment, and sodium nitrate \((\text{NaNO}_3)\)

In this reaction, the compounds exchange ions to create new products. Cadmium sulfide precipitates as a solid pigment, while sodium nitrate remains dissolved in the solution. Understanding chemical reactions and how products result from specific reactants is at the heart of chemistry, allowing us to predict the outcomes of mixing various chemicals.