Question

How many moles of vanadium atoms, \(\mathrm{V},\) are needed to combine with 0.565 mol of \(\mathrm{O}\) atoms to make vanadium pentoxide, \(\mathrm{V}_{2} \mathrm{O}_{5} ?\)

Short answer

The number of moles of vanadium atoms needed are (2 * 0.565) / 5 = 0.226 moles.

Step-by-step solution

Identify the Chemical Equation

First, write the chemical reaction equation between vanadium (V) and oxygen (O) to form vanadium pentoxide (V2O5). The equation is already balanced and can be written as: 2 V + 5 O -> V2O5. This indicates that 2 moles of vanadium react with 5 moles of oxygen to form 1 mole of vanadium pentoxide.

Determine the Mole Ratio

According to the balanced equation, 2 moles of vanadium react with 5 moles of oxygen. Therefore, the mole ratio of vanadium to oxygen is 2:5.

Calculate the Number of Moles of Vanadium

With a mole ratio of 2:5 (V:O) and having 0.565 moles of oxygen, we can calculate the moles of vanadium needed by setting up a proportion: (2 moles V / 5 moles O) = (x moles V / 0.565 moles O). Cross multiply to solve for x, which is the moles of vanadium required.

Perform the Cross Multiplication

2 moles V / 5 moles O = x moles V / 0.565 moles O. Cross multiplying gives: 5 moles O * x moles V = 2 moles V * 0.565 moles O. Solving for x gives: x = (2 moles V * 0.565 moles O) / 5 moles O.

Calculate the Final Amount of Moles

Plugging in the numbers into the equation from the previous step, the calculation becomes: x = (2 * 0.565) / 5. After performing the calculation, we find the number of moles of vanadium.

Key concepts

Understanding Stoichiometry

Stoichiometry is like a recipe for chemists. It's a section of chemistry that involves using relationships between reactants and products in a chemical reaction to determine desired quantitative data. In a balanced chemical equation, the coefficients represent the molar amounts of each substance involved.

For example, in the process of making a cake, stoichiometry tells you how much flour, sugar, eggs, and other ingredients you need. Similarly, in chemical reactions, it shows how many moles of each reactant you need to get a certain amount of product. This relationship is crucial because it allows chemists to predict the outcomes of reactions, design experiments, and even scale up production from a lab test tube to an industrial reactor.

Navigating Chemical Reactions

A chemical reaction involves the transformation of one or more substances into different substances. The periodic table is like a list of ingredients, and a chemical reaction is the cooking process that combines these ingredients to create different dishes — in this case, new compounds.

During these 'cooking' processes, atoms rearrange as bonds are broken and formed. The substances you end up with, known as products, can have different properties from the starting materials, known as reactants. Understanding these transformations requires a clear grasp of chemical equations that neatly portray what happens during a reaction.

Balancing Chemical Equations

Chemical equations must be balanced to comply with the law of conservation of mass, which states that matter cannot be created or destroyed in a closed system. A balanced equation is like a balanced diet — everything is in the correct proportions. If you see an equation like 2 V + 5 O -> V2O5,it tells you exactly how many atoms of each element are involved and ensures that the same number of each atom appears on both sides of the reaction arrow.

So, if you start with 2 vanadium (V) atoms and 5 oxygen (O) atoms, you'll end up with 1 molecule of vanadium pentoxide (V2O5), which is made up of exactly those atoms. No atoms are lost in the process; they're just rearranged. Balancing equations is fundamental in stoichiometry because it sets the stage for all the calculations that follow.

Applying the Mole Ratio

The mole ratio is the heart of stoichiometry, representing the proportion of reactants used and products formed in a chemical reaction. It's extracted directly from the coefficients of a balanced chemical equation and tells us how many moles of one substance react or form in relation to another substance.

In the equation for forming vanadium pentoxide, the mole ratio of vanadium (V) to oxygen (O) is 2:5, drawn from the coefficients 2 and 5, respectively. Knowing this ratio allows you to calculate the amounts of reactants needed or products formed. For instance, if you have a certain number of moles of oxygen, the mole ratio can help you figure out how many moles of vanadium are needed to react with all that oxygen. It's like knowing how many cups of flour you need for every egg to make the perfect cake — without that knowledge, you'd end up with a culinary disaster!