Question

Can one solution have a greater concentration than another in terms of weight percent, but a lower concentration in terms of molarity? Explain.

Short answer

Yes, a solution can have a greater concentration in terms of weight percent and a lower concentration in terms of molarity. This can occur when comparing solutions with different solutes and solvents. For example, a 15% glucose solution has a higher weight percent but a lower molarity (0.833 M) than a 10% NaCl solution (1.71 M). This happens because the weight percent considers the mass of the solute while molarity involves the number of moles of solute in the solution.

Step-by-step solution

Understand weight percent and molarity concentration

Weight percent concentration refers to the mass of a solute divided by the total mass of the solution, multiplied by 100. The formula for weight percent is given by: Weight percent = (Mass of solute / Mass of solution) × 100 Molarity concentration refers to the number of moles of solute present in one liter of solution. The formula for molarity is given by: Molarity = Moles of solute / Volume of solution (in liters)

Consider two solutions with different solutes and solvents

Let's consider two solutions - Solution A and Solution B. For instance, let Solution A be a 10% NaCl (sodium chloride) solution and Solution B be a 15% glucose (C₆H₁₂O₆) solution. We will compare their weight percent and molarity concentrations.

Calculate the moles of solute in each solution

To calculate the moles of solute in each solution, divide the mass of solute by the molar mass of solute for each solution. For Solution A: Mass of NaCl = 100 g (assuming 1000 g of solution) Molar mass of NaCl = 58.44 g/mol Moles of NaCl = \( \frac{100 g}{58.44 g/mol} \) = 1.71 mol For Solution B: Mass of glucose = 150 g (assuming 1000 g of solution) Molar mass of glucose = 180.16 g/mol Moles of glucose = \( \frac{150 g}{180.16 g/mol} \) = 0.833 mol

Calculate molarity for each solution

Now, we will calculate the molarity of each solution by dividing the moles of solute by the volume of the solution. For Solution A (NaCl): Moles of NaCl = 1.71 mol Volume of solution = 1 L (assuming the 1000 g of solution has density similar to water) Molarity of NaCl = 1.71 mol / 1 L = 1.71 M For Solution B (glucose): Moles of glucose = 0.833 mol Volume of solution = 1 L (assuming the 1000 g of solution has density similar to water) Molarity of glucose = 0.833 mol / 1 L = 0.833 M

Compare weight percent and molarity concentrations of the solutions

Solution A has a 10% weight percent concentration, while Solution B has a 15% weight percent concentration. Thus, Solution B has a higher concentration in terms of weight percent. However, when comparing the molarity of both solutions, Solution A has a 1.71 M concentration while Solution B has a 0.833 M concentration. In this case, Solution A has a higher concentration in terms of molarity. Since Solution B has a higher concentration in terms of weight percent but a lower concentration in terms of molarity compared to Solution A, we can conclude that it is indeed possible for a solution to have a greater concentration by weight percent and a lower concentration by molarity.

Key concepts

Weight Percent Concentration

When discussing weight percent concentration, we focus on the amount of solute in a mixture as a percentage of the total solution mass. It's an intuitive expression because it relates directly to weights, which are often used in everyday settings.

The formula is quite straightforward: take the mass of the solute and divide it by the total mass of the solution, then multiply by 100 to get a percentage. For instance, if you dissolve 30 grams of sugar into 120 grams of water, your solution weighs 150 grams in total. To find the weight percent concentration of sugar, you'd compute \( \frac{{30}}{{150}} \times 100 \) to get 20%. Now, because this measurement is dependent on total mass and not volume, it can change with varying conditions, such as temperature, since the density of solutions can change with temperature and thus alter the mass-volume relationship.

A crucial tip for understanding weight percent concentration is to remember it reflects the relative mass of the solute in comparison to the total mixture, largely independent of the solution's volume or the solute's molar mass.

Molarity Concentration

Switching gears, molarity concentration is a measure of how many moles of a substance are present in a liter of solution. It's represented by the symbol 'M' and is often used in chemistry for reactions taking place in a solution because it relates the volume of solution to the amount of substance in terms of its molecular count.

The molarity calculation involves dividing the number of moles of solute by the volume of the solution in liters: \( \text{{Molarity}} = \frac{{\text{{moles of solute}}}}{{\text{{volume of solution in liters}}}} \). For example, if you have 2 moles of salt in 1 liter of water, the molarity is 2 M. In contrast to weight percent concentration, molarity considers the volume of the solution, which makes it sensitive to temperature changes because the solution’s volume can expand or contract with temperature fluctuation causing the molarity to change.

Understanding molarity is essential when mixing solutions to reach a desired reaction rate or when comparing the reactivity of different solutions. Since it relies on the number of molecules able to interact in a given volume, molarity is a key player in predictive chemistry.

Moles of Solute

Moving on to understanding moles of solute, this term delves into the realm of stoichiometry and provides the basis for quantitative measurements in chemistry. A mole is a standard scientific unit for measuring large quantities of very small entities such as atoms, molecules, or other specified particles.

The number of moles of solute in a solution helps determine the solution's strength and capacity to react. The formula to calculate the moles of a substance is to divide the mass of the solute by its molar mass: \( \frac{{\text{{mass of solute}}}}{{\text{{molar mass of solute}}}} \). For instance, if you have 12 grams of carbon (which has a molar mass of 12 g/mol), you have 1 mole of carbon.

Grasping the concept of moles is crucial for any chemistry student because it connects the microscopic scale of atoms and molecules with the macroscopic world that we measure and observe. When conducting experiments or interpreting reactions, knowing the moles of substances involved allows scientists and students alike to predict the outcome of chemical processes and to translate formulas into practical applications.