The first step in solving this question is to convert the mass of each element to moles. This can be done by dividing the given mass of each element by the molecular weight of each element.

After finding the moles of each element, you have to find the smallest whole number ratio of each element. The smallest whole number ratio can be found by dividing moles of each element by the lowest mole quantity (in this case, of oxygen). You are left with carbons, hydrogens, and oxygen. The empirical formula for this compound is .

To find the molecular formula of the compound you need to divide the molecular weight of the actual compound by the molecular weight of the empirical formula. The molecular weight of the empirical formula is:

Dividing the molecular weight of the actual compound () by the molecular weight of empirical formula gives:

This means that the empirical formula must be multiplied by three to get the molecular formula; therefore, the molecular formula is . Compared to the empirical formula, the molecular formula contains more carbon atoms and more oxygen atoms.

A full liter of a one molar solution of sodium hydroxide would contain one mole of sodium ions, or ions. Here, you have only one tenth the volume, so multiply the number in one mole by one tenth.

Now that we have reduced the volume, we need to account for the concentration.

The atomic mass of an element is determined by the proportional mass of each elemental isotope. We know that there are only two isotopes of lithium; therefore, their percentages must add to 100%.

The atomic mass will be equal to the mass of each isotope multiplied by its abundance.

We can substitute an algebraic expression to solve for one of our variables.

Using this value, we can solve for the abundance of the other isotope.

Converting these values to percentages gives us our final answer.

First find the molar mass of water (H2O). You should be comfortable with the molar masses of hydrigen and oxygen from memory to reduce time on the MCAT exam.

Next, solve for moles.

To find the molecular weight (mass) of a molecule, simply add up the atomic weights of each atom within the molecule. The units used will be amu (atomic mass units) for molecular weight and g/mol for molar mass.

To solve, we will need to find the mass of one liter of DEET and use the mass percentage of nitrogen to find the mass of nitrogen represented. Then, the atomic mass of nitrogen can be used to convert this to moles, and Avogadro's number can be used to convert to atoms.

First, find the mass of DEET in a one-liter sample:

Find the mass of nitrogen in 998 grams of DEET by finding the percentage of nitrogen by mass:

Use this mass percentage and atomic mass to find the moles of nitrogen in the one-liter sample.

Use Avogadro's number to find the number of atoms in this sample.

An alternative method would be to convert the grams of DEET to moles, and then from moles to molecules. There is one nitrogen atom per molecule of DEET, so this would method also get you the same answer.

Avogadro's number is used to convert between moles and atoms (or molecules).

This immediately eliminates two answer choices, since moles and molecules in a sample are both contained in the constant. Atoms in a sample of diatomic gas is also easily related to Avogadro's number, as each molecule in the sample will contain exactly two atoms. Avogadro's number can be used to determine the number of moles, molecules, or atoms in a sample of diatomic gas.

Converting grams in a sample to moles allows us to use Avogadro's number to further convert to molecules.

Partial pressure of a gas is directly related to mole fraction, but cannot be used to determine the moles of gas unless the total moles in the sample is known. Partial pressure represents a relationship between the sample and its particular environment, whereas constants govern conversion between moles, grams, atoms, and molecules. Since partial pressure is not directly related to these terms by a constant, Avogadro's number cannot be applied to partial pressure to determine any useful data.

Remember that the empirical formula relies on the ratio of the moles of elements. To get the number of atoms, you would have to multiply the moles of each element by the Avogadro’s number (). You would use this number for every element (Avogadro’s number doesn’t change for each element). This means that the ratio of the number of atoms will be the same as the ratio of the number of moles, and you will get the same empirical formula. There is a constant relationship between the number of moles and the number of atoms in a sample.

The empirical formula for hydrocarbon is , where is the number of carbons. This is only true if the hydrocarbon has no bonds or ring structures. The question states that there is one bond; therefore, the hydrocarbon will lose two hydrogen atoms (). Note that for every bond and every ring the hydrocarbon is associated with the loss of two hydrogen atoms. If we calculate the molecular weight of hydrocarbons with different values () we will find that the nine-carbon hydrocarbon (with bond), nonene, has a molecular weight of . The molecular formula for nonene is ; therefore, the ratio of carbons to hydrogens is 9:18 or 1:2.

You can also calculate the ratio by simply looking at the empirical formula of this molecule (). There will be twice as many hydrogen atoms as carbon atoms; therefore, ratio of carbon to hydrogen will be 1:2.

Start by calculating the percentages of hydrogen in each compound by using molar mass ratios.

Next, take the percentages of the given sample masses to determine the total mass of hydrogen in each.

We see that there is a larger mass of hydrogen in the hydrogen cyanide sample.