Problem 88 - Chemistry Matter and Change

Question

A metal oxide reacts with water to produce a metal hydroxide. What additional information would you need to determine the percent yield of metal hydroxide from this reaction?

Step-by-Step Solution

Answer

To determine the percent yield of the metal hydroxide, you need additional information: the balanced chemical equation for the reaction, the initial amount of the metal oxide (in moles or mass), and the actual yield of the metal hydroxide produced. You can then calculate the percent yield using the following steps: 1) Identify the balanced chemical equation. 2) Calculate the initial moles or mass of the metal oxide. 3) Calculate the theoretical yield of the metal hydroxide. 4) Obtain the actual yield of the metal hydroxide. 5) Calculate the percent yield of the metal hydroxide using the formula: Percent yield = (Actual yield / Theoretical yield) * 100.

Step 1: Identify the balanced chemical equation for the reaction

Determine the balanced chemical equation for the reaction between the metal oxide and water. This will help to find the stoichiometry of the reaction. For example, let's say the balanced chemical reaction is: \(M_2O + 2H_2O \rightarrow 2MOH\) where M represents the metal, M₂O represents the metal oxide, and MOH represents the metal hydroxide.

Step 2: Calculate the initial moles or mass of the metal oxide

You'll need to know the initial amount of the metal oxide used in the reaction (either in moles or mass). If given in mass, you can convert to moles using the molar mass of the metal oxide. To calculate the moles of metal oxide used, use this formula: Moles of metal oxide = Mass of metal oxide used / Molar mass of metal oxide

Step 3: Calculate the theoretical yield of the metal hydroxide

Using stoichiometry, calculate the theoretical yield of the metal hydroxide from the moles of the metal oxide used in the reaction. The ratio of the metal oxide to metal hydroxide, according to the balanced chemical equation, will help with this calculation. For example, in our equation, the ratio of M₂O to MOH is 1:2. To calculate the theoretical yield of the metal hydroxide, use this formula: Theoretical moles of metal hydroxide = (Moles of metal oxide * Ratio of metal hydroxide to metal oxide) Theoretical yield (in grams) = (Theoretical moles of metal hydroxide * Molar mass of metal hydroxide)

Step 4: Obtain the actual yield of the metal hydroxide

Measure or record the actual yield of metal hydroxide produced from the reaction in grams. This is the amount of metal hydroxide that is experimentally obtained from the reaction.

Step 5: Calculate the percent yield of the metal hydroxide

Using the actual yield and the theoretical yield, calculate the percent yield of the metal hydroxide. The formula to calculate the percent yield is: Percent yield = (Actual yield / Theoretical yield) * 100 The percent yield will help you understand the efficiency of the reaction and determine if there are any side reactions or factors affecting the reaction.

Key Concepts

Chemical Reaction

In a chemical reaction, substances known as reactants undergo a transformation to produce new substances called products. Understanding a chemical reaction involves identifying the reactants and predicting the products. For example, a metal oxide reacting with water forms a metal hydroxide. This transformation is often depicted in a balanced chemical equation.

• A balanced chemical equation shows the proportional relationships between reactants and products.
• This is crucial for determining how much of each substance is needed or produced in a reaction.

In our example, the balanced equation is \(M_2O + 2H_2O \rightarrow 2MOH\). This equation indicates that one mole of metal oxide reacts with two moles of water to yield two moles of metal hydroxide. By balancing the equation, we ensure that the number of atoms for each element is the same on both sides of the equation. This reflects the law of conservation of mass.

Stoichiometry

Stoichiometry is the study of the quantitative aspects of chemical reactions. It involves calculations based on the balanced chemical equation to predict how much product will form from a given amount of reactants, or how much reactant is required for a desired amount of product.

• The mole concept is key in stoichiometry, allowing for precise measurements and conversions between mass and moles.
• Stoichiometric calculations help in determining theoretical yields, essential for calculating percent yields.

As in the reaction \(M_2O + 2H_2O \rightarrow 2MOH\), stoichiometry allows us to decide the theoretical yield of \(MOH\) based on the initial amount of \(M_2O\). By knowing the stoichiometric ratios, one can perform these calculations effectively and efficiently.

Theoretical Yield

Theoretical yield is the maximum amount of product that can be formed from a given amount of reactants, according to the stoichiometry of the balanced chemical equation. It assumes that all of the limiting reactant is converted into the desired product, with no side reactions or losses.

• Theoretical yield is calculated using stoichiometric relationships from the balanced equation.
• It represents an ideal scenario and helps assess the efficiency of a reaction through comparison with the actual yield.

For example, if you start with a definite amount of a metal oxide, you use stoichiometry to find out the theoretical amount of metal hydroxide you can expect to produce. If 1 mole of \(M_2O\) can theoretically yield 2 moles of \(MOH\), the theoretical yield in grams would be that number of moles times the molar mass of \(MOH\). This helps set the baseline for evaluating the experimental results.

Actual Yield

Actual yield refers to the amount of product obtained from a chemical reaction in a laboratory setting. Unlike the theoretical yield, the actual yield is usually lower due to various reasons such as incomplete reactions, side reactions, or practical losses during the experiment.

• Actual yield is measured or obtained from the experimental results, usually in grams.
• It's crucial for calculating percent yield, which helps to evaluate the reaction efficiency.

In practice, after conducting the reaction between metal oxide and water, you would measure the amount of metal hydroxide produced. This measured amount, compared with the theoretical yield, contributes to determining the percent yield, indicating the reaction's effectiveness and highlighting any potential issues causing discrepancies.