Question

In an experiment \(0.500 \mathrm{~g}\) of nickel reacted with air to give 0.704 g of nickel oxide. What is the empirical formula of the oxide?

Short answer

The empirical formula of the oxide is \( \text{Ni}_2\text{O}_3 \).

Step-by-step solution

Calculate Moles of Nickel

First, determine how many moles of nickel are present in the original sample. The molar mass of nickel (Ni) is approximately 58.69 g/mol. Use the formula:\[moles = \frac{0.500 \, \text{g}}{58.69 \, \text{g/mol}}. \] Evaluate this to find the moles of nickel.

Moles Calculation

Perform the division:\[moles_{Ni} = \frac{0.500}{58.69} = 0.00852 \, \text{mol}. \] So, there are approximately 0.00852 moles of nickel in the sample.

Calculate Moles of Oxygen

Determine the mass of oxygen combined with nickel by subtracting the mass of nickel from the total mass of nickel oxide:\[m_{O} = 0.704 \, \text{g} - 0.500 \, \text{g} = 0.204 \, \text{g}. \] Use the molar mass of oxygen (approximately 16.00 g/mol) to calculate the moles of oxygen:\[moles_{O} = \frac{0.204}{16.00}. \]

Moles Calculation for Oxygen

Perform the division:\[moles_{O} = \frac{0.204}{16.00} = 0.01275 \, \text{mol}. \] So, there are approximately 0.01275 moles of oxygen.

Determine Moles Ratio

Divide the moles of each element by the smallest number of moles calculated, to determine the simplest whole number ratio:\[\text{Ratio for Ni} = \frac{0.00852}{0.00852} = 1. \]\[\text{Ratio for O} = \frac{0.01275}{0.00852} \approx 1.5. \] This suggests the ratio of nickel:oxygen is 1:1.5.

Find Whole Number Ratios

Since empirical formulas require whole number ratios, multiply each ratio by 2 to eliminate the fractional part:\[\text{Nickel (Ni) ratio} = 1 \times 2 = 2,\]\[\text{Oxygen (O) ratio} = 1.5 \times 2 = 3.\]

Write the Empirical Formula

Based on the whole number ratios determined, the empirical formula for the nickel oxide is \( \text{Ni}_2\text{O}_3 \). This indicates two atoms of nickel for every three atoms of oxygen.

Key concepts

Understanding Moles Calculation

The concept of "moles" is central in chemistry, serving as a bridge between the atomic scale and the macroscopic world we can observe. A mole represents a specific number of particles, usually atoms or molecules, which is approximately 6.022 x 10^23, also known as Avogadro's number. This might sound vast, but it reflects the sheer number of atoms present in even small amounts of matter.
This large number allows chemists to scale up from individual atoms to amounts we can measure and react in the lab.
To calculate moles of a substance, you use the formula:

• Moles = \(\frac{\text{mass of substance (g)}}{\text{molar mass (g/mol)}}\)

In the given problem, we calculated the moles of nickel by dividing the mass of nickel (0.500 g) by its molar mass (58.69 g/mol), yielding approximately 0.00852 moles of nickel.
This method allows us to determine the relative proportion of each element in a compound, which is crucial for identifying the empirical formula of a compound.

The Importance of Molar Mass

Molar mass is a vital concept when studying chemical compounds, as it relates the mass of a substance to the number of moles of its constituent particles. Every element has a unique molar mass, defined as the mass in grams of one mole of atoms of that element.
The molar mass of a compound, such as nickel oxide in this context, is simply the sum of the molar masses of the elements that make up the compound, proportionate to their quantities as dictated by the formula.
For example, the molar mass of nickel is approximately 58.69 g/mol, while that of oxygen is roughly 16.00 g/mol. These values allow for the conversion between the mass of a substance and the amount of moles, an essential step in chemical calculations.
Understanding molar mass ensures accurate moles calculations, as it translates mass measurements into a format chemists can use to deduce composition and reactivity of substances. Whenever you perform a chemical reaction or aim to discover the empirical formula, you can't overlook the need for accurate molar mass values.

Understanding a Chemical Reaction

Chemical reactions involve the transformation of reactants into products, dictated by the rearrangement of atoms. This fundamental concept reveals how substances interact and change, underpinning the field of chemistry.
In the context of the oxidation of nickel, the chemical reaction entails nickel reacting with oxygen from the air to form nickel oxide. This transformation can be expressed with a chemical equation, which symbolically represents the reactants turning into products.

• Reactants: These are the starting substances, in this case, nickel and oxygen.
• Products: These are produced after the reaction, here being nickel oxide.

Understanding the nature of chemical reactions allows for predictions about how substances will interact, the proportion in which they combine, and the resulting compounds formed.
With the empirical formula of the product, we gain insights not just into the makeup of the molecule, but also into the stoichiometry – the quantitative relationships between reactants and products. This knowledge is fundamental for calculating necessary amounts for reactions in both small-scale experiments and large-scale industries.