Question

Estimate an approximate answer for each of the following calculations. Verify your ballpark answer using a calculator: $$\begin{array}{l}\text { (a) } 0.750 \mathrm{~g} \mathrm{Mg} \times \frac{1 \mathrm{~mol} \mathrm{Mg}}{24.31 \mathrm{~g} \mathrm{Mg}}\times\frac{1\mathrm{~mol} \mathrm{MgO}}{1 \mathrm{~mol} \mathrm{Mg}} \times \frac{40.31 \mathrm{~g} \mathrm{MgO}}{1 \mathrm{~mol} \mathrm{MgO}} \\\=? \mathrm{~g} \mathrm{MgO}\end{array}$$

Short answer

The approximate mass of MgO is 1.25 g.

Step-by-step solution

Understand the Calculation

Review each component of the calculation. You have an initial mass of magnesium (Mg) and you are converting it to grams of magnesium oxide (MgO) using a series of conversion factors: moles of Mg, moles of MgO, and finally grams of MgO.

Estimate the Moles of Mg

Start by estimating the number of moles of Mg. Divide the given mass of Mg (0.750 g) by its molar mass (24.31 g/mol). This gives approximations of the number of moles of Mg present.\[ \text{Moles of Mg} \approx \frac{0.750\, \text{g}}{24.31\, \text{g/mol}} \approx 0.031\, \text{mol} \]

Use Stoichiometry to Convert Moles

Using the given stoichiometry from the problem, 1 mole of Mg converts into 1 mole of MgO, so the moles of Mg will be approximately equal to the moles of MgO.\[ \text{Moles of MgO} \approx 0.031\, \text{mol Mg} \]

Convert Moles of MgO to Grams

Now, convert the moles of MgO to grams using its molar mass (40.31 g/mol). Multiply the moles of MgO by the molar mass:\[ \text{Grams of MgO} \approx 0.031\, \text{mol} \times 40.31\, \text{g/mol} \approx 1.25\, \text{g} \]

Verify with a Calculator

Verify the calculation using a calculator to ensure precision:\[ 0.750\, \text{g Mg} \times \left(\frac{1}{24.31}\right) \times 1 \times 40.31 \approx 1.25\, \text{g MgO} \]

Key concepts

Understanding Molar Mass

Molar mass is a foundational concept in stoichiometry, which is the field of chemistry that involves calculating reactants and products in chemical reactions. It refers to the mass of one mole of a substance. A mole itself is a unit used to quantify the amount of a chemical substance. The molar mass of an element is essentially its atomic weight found on the periodic table expressed in grams per mole (g/mol). For example, for magnesium (Mg), which has an atomic weight of 24.31, its molar mass is 24.31 g/mol.
Understanding molar mass is crucial, because it allows us to convert between mass and moles—two different ways of expressing the quantity of a chemical substance. This conversion is essential when dealing with chemical equations where we need precise amounts.
This concept is practically applied when you need to perform calculations like the one in the exercise, where you are starting with a mass of magnesium and need to convert it into a corresponding mass of magnesium oxide.

Exploring Mole Conversions

Mole conversions are a key operation in stoichiometry. They allow us to translate between the number of moles of a substance and its mass, utilizing the relationship defined by the substance's molar mass. This is vital for interpreting and balancing chemical equations, which specify the amount of reactants needed to form products in a reaction.
When you are given a mass (for instance, the 0.750 grams of Mg mentioned in the exercise), and need to find how many moles that equates to, you would divide the mass by the molar mass (24.31 g/mol for Mg). This type of conversion helps you understand how much of the substance is present in terms that connect directly to chemical reaction equations, which are typically balanced on a molar basis.
By mastering mole conversions, you can ensure the right proportions of substances in a reaction, preparing you to handle more complex chemical stoichiometry tasks.

Insight into Chemical Reactions

Chemical reactions are processes where reactants are transformed into products. In the context of stoichiometry, understanding the balanced chemical equation is crucial. This tells you the proportion in which reactants mix and products form, based on moles.
In the exercise provided, you see a typical reaction where magnesium (Mg) combines with oxygen to form magnesium oxide (MgO). The stoichiometric relationship here is straightforward: 1 mole of Mg yields 1 mole of MgO. This one-to-one ratio is a direct consequence of balancing the chemical equation, ensuring mass conservation.
These balanced equations allow chemists to predict the amounts of products formed from given reactants, as shown in the last step of the exercise — converting moles of MgO to grams utilizing its molar mass. Understanding how to interpret and use these equations is fundamental for accurately predicting the outcome of a chemical reaction.