Question

Two substances, W and X, react to form the products Y and Z. Table 11.2 shows the moles of the reactants and products involved when the reaction was carried out. Use the data to determine the coefficients that will balance the equation \(\mathrm{W}+\mathrm{X} \rightarrow \mathrm{Y}+\mathrm{Z}\)

Short answer

After analyzing the given moles of reactants and products, we can find the coefficients for the balanced chemical equation by setting up mole ratio equations for reactants and products. Solve these equations for the unknown coefficients and choose integer values for a and c such that b and d are also integers. Finally, plug the values for a, b, c, and d into the balanced chemical equation and verify that the atoms of each element are conserved on both sides of the equation. The resulting balanced chemical equation will be in the form of \(aW + bX \rightarrow cY + dZ\), with the appropriate integer coefficients for each substance. Note that specific mole values are needed from the given table to calculate the correct coefficients.

Step-by-step solution

Identify the given information from the table

We are given a table with the moles of reactants and products. Let's denote the coefficients of the balanced chemical equation as follows: \(aW + bX \rightarrow cY + dZ\) The moles for reactants and products are described as: - Moles of W: \(M_W\) - Moles of X: \(M_X\) - Moles of Y: \(M_Y\) - Moles of Z: \(M_Z\) We are looking to find \(a, b, c\), and \(d\).

Set up the mole ratio equations

We will now set up the mole ratio equations using the mole ratios from the given data: For reactants: \(\frac{M_W}{a} = \frac{M_X}{b}\) For products: \(\frac{M_Y}{c} = \frac{M_Z}{d}\)

Solve for the unknown coefficients

We will now solve the above equations for the unknown coefficients: For reactants: \(b = \frac{M_X}{M_W} \cdot a\) For products: \(d = \frac{M_Z}{M_Y} \cdot c\) Solve the above equations in terms of a and c, respectively.

Choose values for a and c

Choose integer values for a and c, such that the coefficients, b and d, are also integers. You can start by choosing a = 1 and c = 1, and then adjust the values accordingly.

Check if the chemical equation is balanced

Plug the values for a, b, c, and d into the balanced chemical equation: \(aW + bX \rightarrow cY + dZ\) Verify that the atoms of each element are conserved on both sides of the equation. If not, adjust the coefficients accordingly and recheck.

Write the balanced chemical equation

Once the chemical equation is balanced, write the final balanced chemical equation with the appropriate coefficients for each substance: \(aW + bX \rightarrow cY + dZ\) Remember to replace a, b, c, and d with the integer coefficients obtained in step 4 and confirmed in step 5. Note: This is a general guideline for solving the problem, as the specific values of moles for reactants and products are not provided in the question. To complete the solution, you would need to use the actual mole values from the given table to calculate the correct coefficients.

Key concepts

Mole Ratios

Mole ratios are crucial in balancing chemical equations and understanding reactions. They represent the proportions of reactants and products in a chemical reaction. When substances react, they do so in specific ratios according to their chemical equation. This is where mole ratios come into play. By comparing the moles of reactants to each other and to the products, we can determine the relative quantities required or produced.

For example, in a reaction involving substances W, X, Y, and Z, if you know the moles of each, you can find the ratios. These ratios help you simplify complex reactions and figure out the balance.

To determine mole ratios, consider:

• Comparing moles of reactants to each other. For instance, if you have a ratio like \(\frac{M_W}{a} = \frac{M_X}{b}\), it tells you how many moles of W react with X.
• Comparing moles of products, such as \(\frac{M_Y}{c} = \frac{M_Z}{d}\), which shows the production relationship between Y and Z.

Understanding these ratios is key to solving for the coefficients in a balanced equation, ensuring you have the right amount of each substance for the reaction to proceed effectively.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into new substances, called products. During these transformations, the atoms in reactants are reorganized to form different compounds. A balanced chemical equation represents this, showing the number of moles of each reactant and product involved.

In our example with substances W, X, Y, and Z, the equation \(\mathrm{W} + \mathrm{X} \rightarrow \mathrm{Y} + \mathrm{Z}\) symbolizes the process where reactants W and X create products Y and Z.

Key concepts to understand in chemical reactions involve:

• The conservation of mass, meaning that the number of each type of atom must be the same on both sides of the equation.
• Interpreting the coefficients in a chemical equation; these depict the moles of substances involved, like the unknowns a, b, c, and d in our example. Balancing these coefficients ensures the reaction equation is correct.
• Typical reactions include synthesis, decomposition, single replacement, and double replacement, all involving different types of reactant-product interactions.

Grasping these concepts helps in predicting product formation and understanding the fundamental nature of chemical reactions.

Stoichiometry

Stoichiometry is the part of chemistry that deals with calculating the amounts of reactants and products in a chemical reaction. It connects the balanced equation coefficients, which serve as mole ratios, to practical measurements like grams or liters.

In the example of balancing \(\mathrm{W} + \mathrm{X} \rightarrow \mathrm{Y} + \mathrm{Z}\), stoichiometry helps us quantify exactly how much of W or X is necessary to fully react and yield Y and Z.

The essential steps in stoichiometry involve:

• Using balanced chemical equations to interpret the mole ratios between reactants and products.
• Converting measurements from grams to moles, using the molar mass of substances (grams per mole).
• Applying mole-to-mole ratios as conversion factors in calculations, allowing for the determination of desired reactant or product amounts.

Mastering stoichiometry enables you to predict the outcomes of reactions and adjust the quantities of substances accordingly. This application is fundamental in lab settings and industrial processes where precise chemical quantities are crucial for success.