Question

Read carefully. Twice as much as one million trillion is two million trillion. One thousand times as much is 1000 million trillion. One million times as much is \(1,000,000\) million trillion, which is the same as one trillion trillion. Thus, one trillion trillion is one million times greater than a million trillion. Got that? So how many more water molecules than impurity molecules are there in a glass of water that is \(99.9999\) percent pure?

Short answer

There are 999,998 more water molecules than impurity molecules.

Step-by-step solution

Understanding the Purity Percentage

A glass of water is stated to be 99.9999% pure. This means that 99.9999% of the molecules in the glass are water molecules, and the remaining is impurity molecules.

Calculating the Proportion of Impurity

Since the water is 99.9999% pure, the percentage of impurity is 100% - 99.9999% = 0.0001%.

Expressing the Proportion as a Fraction

Convert the percentage of impurity to a fraction: \[ 0.0001\% = \frac{0.0001}{100} = \frac{1}{1,000,000} \] This means that for every 1,000,000 molecules in the glass, there is 1 impurity molecule.

Calculating Number of Water Molecules

Since 1 impurity molecule corresponds to 1,000,000 molecules in total and there's 1 impurity, the remaining 999,999 are water molecules.

Determining the Excess of Water Molecules

Subtract the number of impurity molecules from total water molecules:\[ 999,999 - 1 = 999,998 \] So, there are 999,998 more water molecules than impurity molecules in each group of 1,000,000 molecules.

Key concepts

Molecular Purity

When we talk about molecular purity, we're referring to the chemical composition of a substance. Molecular purity is a measure of how pure a substance is at the molecular level. It's like saying how many molecules in a substance are of the type we are interested in—in this case, water molecules, as opposed to any impurities.

If water is 99.9999% pure, it means nearly all molecules in that water should indeed be water molecules. The rest would be impurities. This is critical in chemistry and other fields because the presence of impurities can significantly affect the properties of a substance. Knowing the molecular purity helps us understand the possible behaviors and reactions a substance might undergo.

• High molecular purity indicates fewer impurities, meaning better quality or performance in reactions.
• Even tiny fractions of impurity can influence reactions in sensitive processes.

Water Molecules

Water is composed of two hydrogen atoms bonded to one oxygen atom making the formula H₂O. In a glass of pure water, you would expect that almost all the molecules to be water molecules, especially if the purity is high like 99.9999%.

Water molecules are incredibly small—so small, in fact, that just a drop of water contains billions of them. Despite their tiny size, they have a massive impact on our daily lives and sustain ecosystems globally. In calculating how many molecules are in a sample, chemists often use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules per mole, to determine how many water molecules exist in a given sample. This is essential for translating molecular purity percentages into actual counts of molecules.

Percent Composition

Percent composition in chemistry refers to the percentage by mass of each element in a compound or the percentage by volume or molecule count in mixtures. When dealing with water purity, percent composition is used to express how much of the substance is water and how much are impurities.

For instance, water being 99.9999% pure means if you have a million molecules in a sample, 999,999 of those are water molecules, while only one molecule is considered an impurity. This provides a straightforward way to communicate purity and compare samples.

• Percent composition allows easy comparison of different mixtures in terms of purity and impurity.
• In high-purity situations, even small percentages of impurity, like 0.0001%, can be relevant.

Impurity Percentage

The impurity percentage of a substance indicates how much of it is made up of unwanted or foreign particles. In highly purified water, as in the example, the impurity percentage is very low—only 0.0001% in this case.

Understanding impurity percentage helps anticipate the effects low-grade purity might have on chemical reactions. In high precision contexts, even a minimal impurity percentage can make a big difference. This is particularly important in fields like pharmaceuticals, where impurities can affect drug efficacy or safety.

• Impurity percentages are usually calculated by subtracting the purity percentage from 100%.
• For water, a 0.0001% impurity translates to one part impurity per million parts; it's a way to quantify purity precisely.