Question

A gaseous hydrogen- and carbon-containing compound is decomposed and found to contain \(85.63 \% \mathrm{C}\) and \(14.37 \% \mathrm{H}\) by mass. The mass of \(258 \mathrm{~mL}\) of the gas, measured at STP, was 0.646 g. What is the molecular formula of the compound?

Short answer

The molecular formula of the compound is CH.

Step-by-step solution

Determine the mass of C and H in a 100 g sample

As the percentage composition is given by mass, assume a 100 g sample of the compound. The mass of carbon in the compound is then 85.63 g and the mass of hydrogen is 14.37 g.

Convert mass to moles

Using the molar mass of C (12.01 g/mol) and H (1.008 g/mol), convert the mass of each element to moles. For carbon: 85.63 g / 12.01 g/mol. For hydrogen: 14.37 g / 1.008 g/mol.

Determine the mole ratio

Divide the moles of each element by the smallest number of moles calculated in Step 2 to find the simplest whole number ratio of atoms in the compound.

Find the volume of one mole of gas at STP

At STP (standard temperature and pressure), 1 mole of any gas occupies 22.414 L (22,414 mL).

Calculate the molar mass of the gas

Using the density formula (mass/volume), calculate the molar mass of the gas: Multiply the mass of the gas by the volume of 1 mole of gas at STP, then divide by the volume given in the problem (258 mL).

Determine the molecular formula from the empirical formula and molar mass

Divide the molar mass calculated in Step 5 by the molar mass of the empirical formula obtained in Step 3 to get a multiplier. Then multiply the numbers of each atom in the empirical formula by this multiplier to find the molecular formula.

Key concepts

Percentage Composition by Mass

Understanding the percentage composition by mass is crucial when analyzing chemical compounds. It tells us what portion of a compound's mass is made up by each individual element. To grasp this concept, imagine you have a pizza divided into slices of different sizes representing various ingredients. Each slice's size compared to the whole pizza is like the mass percentage of each element in a compound.

To determine the percentage composition by mass, you would weigh each ingredient and then express its mass as a percentage of the total mass of the pizza. Similarly, when given a chemical compound, calculate the mass of each element present and then determine what percentage it contributes to the total mass.

Molar Mass Calculation

Knowing how to calculate molar mass is like understanding the weight of a basket of fruits where each type of fruit has its own weight. The molar mass is the weight of one mole (a specific number, known as Avogadro's number, of molecules or atoms) of a substance.

To calculate the molar mass, look at the atomic weights of each element, found on the periodic table, and add them together according to the formula of the substance. It is essential to do this to transition from the mass of a substance to the amount in moles, which is necessary for understanding the substance's relationship with other chemicals in a reaction.

Mole Ratio

The mole ratio is the bridge between different chemicals in a reaction, linking their quantities in a clear and proportional manner. It’s as if you’re using a blueprint to build a model; the blueprint provides the ratio of materials you need, just as the mole ratio tells you how many particles of one chemical react with another.

To find the mole ratio, you calculate the moles of each element and then express these quantities in the smallest whole number ratio. This simplified ratio is the essence of the compound's formula, providing insight into the fundamental proportions of its constituent elements.

STP Conditions

In chemistry, STP conditions are a standard set of conditions for measuring gases, much like using a specific setting on your air conditioner to compare performance on different days. STP stands for Standard Temperature and Pressure, which is defined as 0 degrees Celsius (273.15 Kelvin) and 1 atmosphere pressure.

Under STP conditions, any gas occupies 22.414 liters per mole, which is a helpful constant when you need to calculate gas volumes or densities. Knowing this volume allows us to relate the physical volume of a gas to the amount in moles, making calculations standardized across various conditions.

Gas Density and Molar Mass Relationship

The relationship between gas density and molar mass can be seen as a way to determine how heavy a 'cloud' is. Density is the mass of a substance per unit volume. For gases, we can use this concept to find out how much one mole of a gas weighs by measuring the mass of a known volume of the gas.

By rearranging the density formula, you can use the gas’s measured mass and its volume at STP to find its molar mass. This relationship is crucial when identifying an unknown gas, as it allows you to work backwards from physical measurements to determine the gas's molecular formula, which is a key characteristic in identifying the substance.