Question

A metal oxide having \(40 \%\) oxygen. The equivalent weight of metal is: (a) 24 (b) 12 (c) 36 (d) 20

Short answer

The equivalent weight of the metal is 12.

Step-by-step solution

Define the percent composition formula

The formula for percent composition is given by: \( \text{Percent Composition} = \left( \frac{\text{mass of element}}{\text{total mass of compound}} \right) \times 100 \). In this problem, we have the percent composition of oxygen in the metal oxide as \(40\%\).

Express mass of oxygen and metal

Since the metal oxide is composed of metal and oxygen only, let's denote the mass of the oxygen as \(m_{\text{Oxygen}} = 16\) (as the atomic weight of oxygen is 16 u), and the mass of the metal as \(m_{\text{Metal}} = M\).

Set up equation using percent composition

Since the metal oxide has \(40\%\) oxygen by mass, set the expression for the percent composition: \( 40 = \left( \frac{16}{M + 16} \right) \times 100 \).

Solve for the mass of the metal oxide

From the equation in step 3: \( 40 = \left( \frac{16}{M + 16} \right) \times 100 \) \( \Rightarrow \) \( M + 16 = \frac{1600}{40} \) \( \Rightarrow \) \( M + 16 = 40 \).

Calculate the mass of the metal (M)

Rearrange the equation: \( M = 40 - 16 = 24 \). So the mass of the metal is 24 u.

Determine the equivalent weight of the metal

The equivalent weight of metal is its atomic weight divided by its valency. Assume the valency of the metal is 2 (as it commonly is for many metal oxides): \( \text{Equivalent weight} = \frac{24}{2} = 12 \).

Key concepts

Percent Composition

Percent composition is a fundamental concept in chemistry that allows you to understand the proportion of each element within a compound. It's a straightforward calculation intended to express the relative amount of each element in percentage terms. To find the percent composition, you use the formula:\[\text{Percent Composition} = \left( \frac{\text{mass of element}}{\text{total mass of compound}} \right) \times 100\]In a compound, percent composition can tell you how much of each element makes up the total substance. For example, in a metal oxide with 40% oxygen, this means that for every 100 grams of metal oxide, 40 grams are oxygen. This kind of calculation helps you understand the makeup of compounds, which is essential for predicting reactions and properties of substances. It’s a crucial tool in both theoretical analyses and practical applications in chemistry.

Metal Oxide

Metal oxides are compounds composed of metal elements combined with oxygen. These occur commonly in nature and are significant in various chemical processes and industrial applications. - **Formation**: Metal oxides form when metals react with oxygen. For example, iron reacts with oxygen to form iron (III) oxide, rust. - **Properties**: They typically have high melting points and are often used as catalysts or supports in industrial processes. Many metal oxides are also bases and will react with acids to form salts and water. - **Applications**: They're used in a range of industries, such as ceramics, electronics, and construction. Zinc oxide, for instance, is used in sunscreens, as it reflects UV light. Understanding metal oxides' composition is essential, especially in terms of calculating percent composition and determining their roles in broader chemical reactions.

Atomic Weight

Atomic weight, also known as relative atomic mass, is the weighted average mass of an atom of an element. It's measured in atomic mass units (u) or daltons and accounts for the presence of isotopes. - **Calculation**: The atomic weight of an element takes into account the masses of its isotopes and their abundances. Thus, it's not a whole number. - **Example**: Oxygen has an atomic weight of approximately 16 u, as most oxygen atoms have a mass of 16 u. However, this is an average that accounts for all isotopes found in nature. Atomic weight is crucial when identifying the composition of compounds and calculating properties like molar masses. It lays the groundwork for most stoichiometric calculations in chemistry.

Valency

Valency is a measure of an element's ability to bond with other atoms. It reflects how many electrons an atom can gain, lose, or share when forming chemical bonds. - **Understanding Valency**: Typically, metals in oxides exhibit a valency that allows them to donate electrons to oxygen, forming ionic or covalent bonds. A common valency for metal oxides is 2, as seen in calcium oxide (CaO), where calcium exhibits a valency of 2. - **Role in Compounds**: Valency determines how atoms will interact with one another, forming compounds through ionic or covalent bonds. It is instrumental in predicting molecular structure and behavior. Valency is a key concept when calculating equivalent weights. The equivalent weight of an element in a compound, like a metal in a metal oxide, is derived by dividing the atomic weight by the valency.