Question

A \(2.241-\mathrm{g}\) sample of nickel reacts with oxygen to form \(2.852 \mathrm{~g}\) of the metal oxide. Calculate the empirical formula of the oxide.

Short answer

The empirical formula of the oxide is \( \text{NiO} \)

Step-by-step solution

Calculate the mass of oxygen

Find the mass of oxygen by subtracting the mass of nickel from the mass of the metal oxide. The formula for this step is: mass of oxygen = mass of metal oxide - mass of nickel.

Calculate moles of nickel and oxygen

Convert the mass of nickel and oxygen to moles by using their respective molar masses. Nickel has a molar mass of approx. 58.69 g/mol and oxygen (O) has a molar mass of 16 g/mol (since oxygen in the oxide is O, not O2). The formula for calculating moles is: moles = mass (g) / molar mass (g/mol).

Determine the mole ratio

To find the empirical formula, we need the simplest whole number ratio of moles of nickel to moles of oxygen. Divide the moles of each element by the smallest number of moles calculated from step 2.

Write the empirical formula

Use the mole ratio to write the empirical formula, which will have the form \( \text{Ni}_x\text{O}_y \) where \( x \) and \( y \) are the mole ratios of nickel and oxygen, respectively.

Key concepts

Stoichiometry

Stoichiometry is the section of chemistry that pertains to the quantitative relationships between the substances consumed and produced in chemical reactions. In essence, it allows chemists to predict the amounts of substances needed and formed in a chemical reaction. When determining an empirical formula, stoichiometry is used to calculate the simplest whole-number ratio of atoms within a compound based on the masses of elements present in a sample.

Consider the sample problem involving nickel and oxygen; the task is to determine the empirical formula of nickel oxide produced. Using stoichiometry, we first find the amount of oxygen by subtracting the nickel's mass from the total mass of the compound. Then, we convert these masses into moles, which serve as the bridge in stoichiometry for relating the mass of elements to the number of atoms they contain. Understanding the concept of stoichiometry is crucial for solving empirical formula problems, as it provides the framework for converting mass measurements into mole ratios, which are then used to derive the chemical formula.

Molar Mass

The concept of molar mass is foundational when it comes to understanding chemical reactions on a quantitative level. It is defined as the mass of one mole of a substance, typically expressed in units of grams per mole (g/mol). Every element has its own unique molar mass, which can be found on the periodic table.

In the nickel oxide problem, you need the molar masses of nickel and oxygen to convert the mass of each element to moles. Knowing that the molar mass of nickel is approximately 58.69 g/mol and that of oxygen is 16 g/mol is essential for accurate moles calculation. It's like knowing the conversion rate between two currencies when traveling to a different country—the molar mass lets you 'convert' between grams and moles, thus enabling you to work within the universal 'currency' of moles in chemistry.

Moles Calculation

Calculation of moles is a straightforward but vital step in empirical formula determination. The number of moles represents the number of particles, be they atoms or molecules, and is calculated by dividing the mass of a substance by its molar mass. The mathematical foundation for this is the formula: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \).

For the nickel oxide example, once you have the mass of nickel and oxygen, you would divide each by their respective molar masses to find the number of moles present in the sample. The resulting figures are the cornerstone for finding the empirical formula because they reflect the actual ratio of atoms in the compound.

Chemical Formula

Finally, the chemical formula crystallizes the stoichiometric relationships between elements in a compound. It indicates the types and numbers of atoms that compose the substance. An empirical formula is a specific type of chemical formula that shows the simplest whole-number ratio of atoms in the compound.

In the context of the given exercise, the empirical formula of nickel oxide will be derived by taking the simplest whole-number ratio of the moles of nickel to moles of oxygen. This process may involve dividing both values by the smallest number of moles present, ensuring that the ratio reflects the essence of the compound without any fractional or decimal numbers. The empirical formula is fundamental to understanding the composition of compounds and plays an integral role in the study of stoichiometry and chemical reactions.