Question

When \(3.269 \mathrm{~g}\) of zinc is heated in pure oxygen, the sample gains \(0.800 \mathrm{~g}\) of oxygen in forming the oxide. Calculate the empirical formula of zinc oxide.

Short answer

The empirical formula of zinc oxide is ZnO, based on the given information of zinc gaining 0.800 g of oxygen when 3.269 g of zinc is heated in pure oxygen. This gives a 1:1 mole ratio between zinc and oxygen in the compound.

Step-by-step solution

Convert mass to moles

First, we need to convert the given mass of zinc and oxygen to moles. We will use the molar mass of each element to do this. The molar mass of zinc (Zn) is 65.38 g/mol, and the molar mass of oxygen (O) is 16.00 g/mol. For zinc: \(moles (Zn) = \frac{3.269 ~ g}{65.38 ~ g/mol} = 0.0500 ~ mol\) For oxygen: \(moles (O) = \frac{0.800 ~ g}{16.00 ~ g/mol} = 0.0500 ~ mol\)

Determine the mole ratio

Now that we have the moles of each element, we can find the ratio between the number of moles of zinc and the number of moles of oxygen. \(\frac{moles (Zn)}{moles (O)} = \frac{0.0500 ~ mol}{0.0500 ~ mol} = 1 \) This ratio means that for every 1 mole of zinc, we have 1 mole of oxygen.

Write the empirical formula

As we found out in Step 2, the ratio between the number of moles of zinc and the number of moles of oxygen is 1:1. This means that the empirical formula for zinc oxide is: ZnO

Key concepts

Zinc Oxide

Zinc oxide is a fascinating compound that's essential in various industrial and commercial applications. It is formed through a simple yet intriguing chemical reaction between zinc (Zn) and oxygen (O). To create zinc oxide, we usually heat zinc in the presence of pure oxygen, and a chemical bond forms between the two elements.
As part of this process, zinc and oxygen react in a straightforward 1:1 ratio, resulting in the empirical formula for zinc oxide, which is ZnO. This means that one atom of zinc pairs with one atom of oxygen to form a molecule of zinc oxide.
Zinc oxide is widely used as a semiconductor, in the production of rubber, and even in sunscreens. Its role in protecting our skin from UV rays is due to its reflective and absorptive properties. This compound is an excellent example of how empirical formulas are calculated in chemistry and shows the importance of understanding chemical reactions.

Mole Ratio

The mole ratio is a fundamental concept in chemistry that helps in understanding reactions and compounds. It's a way to express the proportions between different chemical species in a reaction. When determining the empirical formula of a compound, we use the mole ratio to balance the number of atoms or moles of each element involved.
In the case of forming zinc oxide, we calculate the mole ratio between zinc and oxygen by converting the mass of each element to moles. Using the given weights and their respective molar masses, we found that 3.269 grams of zinc converts to 0.0500 moles, and 0.800 grams of oxygen turns into 0.0500 moles.
The mole ratio here is straightforward: for zinc and oxygen, the calculated moles both equal 0.0500, resulting in a 1:1 ratio. This tells us that for every mole of zinc reacting, one mole of oxygen is required, leading to the empirical formula ZnO. Understanding mole ratios is crucial as it provides insight into the stoichiometry of a reaction, which is essential for predicting the quantities of reactants and products involved.

Chemical Composition

Understanding chemical composition is key to grasping how substances combine to form new compounds. It involves knowing the types and quantities of each element that make up a compound. In chemistry, this is often represented by an empirical formula, which is a simplified ratio of the elements involved.
For zinc oxide, the chemical composition is analyzed by measuring the masses of zinc and oxygen that combine to form it. Given the masses obtained from the experiment — 3.269 grams of zinc and 0.800 grams of oxygen — we calculate their mole quantities using their molar masses.
The calculated mole quantities are both 0.0500, leading to an equal mole ratio and an empirical formula of ZnO. This reflects the chemical composition clearly, showing that zinc oxide consists of an equal number of zinc and oxygen atoms. The knowledge of chemical composition is fundamental not only in chemistry, but also in fields like materials science and pharmacology, where precise formulas are crucial for product development and formulation.