Question

Element \(\mathrm{A}\) reacts with oxygen to form a compound \(\mathrm{A}_{2} \mathrm{O}_{3} .\) If \(0.359\) gram of a compound contains \(0.128 \mathrm{~g}\) of oxygen, atomic weight of \(\mathrm{A}\) will be (1) 51 amu (2) \(43.08\) amu (3) \(49.7\) amu (4) \(47.9 \mathrm{am} \mathrm{u}\)

Short answer

The atomic weight of \( A \) is approximately 43.08 amu.

Step-by-step solution

Determine the mass of element \( A \)

Given that the total mass of the compound is \( 0.359 \) grams and it contains \( 0.128 \) grams of oxygen, the mass of element \( A \) can be found by subtracting the mass of oxygen from the total mass. \(\text{Mass of } A = 0.359 \text{ g} - 0.128 \text{ g} = 0.231 \text{ g}\)

Calculate the moles of oxygen

Use the atomic weight of oxygen (16 g/mol) to calculate the moles of oxygen in the compound. \(\text{Moles of oxygen} = \frac{0.128 \text{ g}}{16 \text{ g/mol}} = 0.008 \text{ mol}\)

Find the moles of element \( A \)

Since the chemical formula of the compound is \( A_2 O_3 \, \single\), the mole ratio of \( A \) to oxygen is 2:3. Using this ratio, calculate the moles of \( A \): \(\text{Moles of } A = \frac{2}{3} \times 0.008 \text{ mol} = 0.00533 \text{ mol}\)

Compute the atomic weight of element \( A \)

Atomic weight can be found by dividing the mass of \( A \) by the moles of \( A \): \(\text{Atomic weight of } A = \frac{0.231 \text{ g}}{0.00533 \text{ mol}} = 43.32 \text{ g/mol}\) This result is closest to option (2).

Key concepts

Mass and Moles Relationship

Understanding the relationship between mass and moles is crucial in chemistry. The mass of a substance can be converted to moles using its molar mass, which is the mass of one mole of that substance in grams. For example, the atomic weight of oxygen is 16 g/mol. This means that one mole of oxygen atoms weighs 16 grams.

To find the moles of a substance, you can use the formula:
\( \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \)

In the original exercise, we calculated the moles of oxygen in the compound by dividing the mass of oxygen (0.128 grams) by its atomic weight (16 g/mol). This gave us 0.008 moles of oxygen. Once you have the moles, you can use them to find the moles of other elements in the compound, helping you understand the compound's composition.

Converting between mass and moles allows chemists to quantify substances involved in chemical reactions and predict the amounts needed or produced accurately.

Mole Ratio

The mole ratio is a bridge in chemical equations that connects the amounts of different substances. It comes from the coefficients in a balanced chemical equation and shows how many moles of one substance react with or produce another.

In the original exercise, the compound was \(\text{A}_2 \text{O}_3\). This formula tells us that for every 2 moles of element A, there are 3 moles of oxygen. This 2:3 ratio is the mole ratio for this compound.

To use the mole ratio, follow these steps:

• Find the moles of one substance (we found moles of oxygen first).
• Use the mole ratio to find the moles of another substance (we used the 2:3 ratio to find moles of A).
• Convert moles back to grams if needed.

In the exercise, we calculated the moles of element A as \( \frac{2}{3} \times 0.008 \text{ mol} = 0.00533 \text{ mol} \). Knowing the mole ratio helps determine how elements combine in given proportions to form compounds.

Chemical Formulas

Chemical formulas provide a shorthand way to represent the types and numbers of atoms in a compound. For instance, \(\text{A}_2 \text{O}_3\) tells us there are 2 atoms of element A for every 3 atoms of oxygen.

Understanding chemical formulas helps in figuring out how a compound is constructed. Here's what we can learn from a formula like \(\text{A}_2\text{O}_3\):

• The subscripts indicate the number of each type of atom. In this case, 2 atoms of A and 3 atoms of O.
• Knowing the mole ratio (from the formula) helps us calculate the amount of each component in a sample.
• It shows the proportions in which elements combine to form the compound.

In the exercise, the formula \(\text{A}_2 \text{O}_3\) allowed us to relate the masses and moles of the elements in the compound. This made it possible to accurately calculate the atomic weight of element A by using the given masses and the known atomic weight of oxygen.

Understanding formulas is essential for solving problems in chemistry, predicting compound formations, and performing laboratory experiments.