Question

\(2.82 \mathrm{~g}\) of glucose is dissolved in \(30 \mathrm{~g}\) of water. The mole fraction of glucose in the solution is (a) \(0.01\) (b) \(0.99\) (c) \(0.52\) (d) \(1.66\)

Short answer

The mole fraction of glucose is (a) 0.01.

Step-by-step solution

Calculate the molar mass of glucose

To find the moles of glucose, first calculate its molar mass. Glucose (C6H12O6) has a molar mass which is the sum of the atomic masses of all its atoms: 6 carbons (C), 12 hydrogens (H), and 6 oxygens (O). The molar mass of carbon is 12.01 g/mol, of hydrogen is 1.01 g/mol, and of oxygen is 16.00 g/mol. Therefore, the molar mass of glucose = (6 * 12.01) + (12 * 1.01) + (6 * 16.00) g/mol.

Calculate the moles of glucose

Using the molar mass from step 1, calculate the moles of glucose. Moles of glucose = mass of glucose (g) / molar mass of glucose (g/mol).

Calculate the mole fraction of glucose

The mole fraction of glucose is calculated by dividing the moles of glucose by the total moles of the solution (moles of glucose plus moles of water). Since water is the solvent and is present in a large amount, its amount in moles needs to be calculated using its molar mass (18.015 g/mol). Calculate the moles of water using its mass and molar mass. Then add the moles of water to the moles of glucose to find the total moles. Finally, divide the moles of glucose by the total moles to find the mole fraction of glucose.

Key concepts

Molar Mass

Understanding the molar mass of a substance is crucial for studying and working with chemical reactions. Essentially, the molar mass is the weight of one mole (Avogadro's number, or approximately 6.022 x 10²³ particles) of a given substance. This mass is usually expressed in grams per mole (g/mol) and is calculated by summing the atomic masses of all the atoms in a molecule.

For example, glucose (C₆H₁₂O₆) consists of carbon (C), hydrogen (H), and oxygen (O) atoms. Calculating its molar mass involves multiplying the number of each type of atom by its respective atomic mass (found on the periodic table), and then adding these values together. The precise calculation of molar mass is the foundation for many chemistry problems, as it allows chemists to convert between mass and moles of a substance, enabling the quantification of reactants and products in a chemical reaction.

Calculating Moles

The concept of moles is central to chemistry because it provides a bridge between the atomic scale and the macroscopic scale. When faced with a problem that requires calculating moles, one should remember the formula: moles = mass of the substance (g) / molar mass of the substance (g/mol).

It's important to be accurate in these calculations as moles directly relate to the number of particles in a sample. This can affect the stoichiometry of chemical reactions and the preparation of solutions. Remember to always use the molar mass of the substance accurately calculated, as any error in the molar mass will propagate through to the final calculation of moles.

Solution Concentration

Solution concentration quantifies the amount of solute in a given amount of solvent or solution. There are several ways to express this concentration, such as molarity, molality, mass percent, or mole fraction.

In this case, we focus on mole fraction, which is the ratio of the number of moles of one component to the total number of moles of all components in the solution. It is a dimensionless quantity and an important concept in colligative properties. It's also used to calculate partial pressures in gas mixtures according to Raoult's law. Correct calculation of solution concentrations is pivotal in preparing laboratory solutions, pharmaceutical dilutions, and in many industrial processes.

Chemistry Problem Solving

Chemistry problems often involve several concepts that need to be applied in a logical sequence. Effective problem-solving in chemistry starts with identifying the known and unknown quantities and the concepts applicable to the problem.

For calculating mole fraction in a solution, a methodical approach is essential. Begin by computing molar masses and the number of moles of each component. It's also important to keep track of the units and ensure consistency throughout the calculation. Having a clear understanding of the relationships between units like grams, moles, and liters, as well as the property you are solving for (in this case, mole fraction), is key to success. Practical problem-solving skills are enhanced by frequent practice of assorted chemistry problems, which also aids in reinforcing the foundational concepts required for complex tasks.