Question

An aqueous solution is \(6.00 \%\) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) by mass, with \(d=0.988 \mathrm{g} / \mathrm{mL} .\) What is the molarity of \(\mathrm{CH}_{3} \mathrm{OH}\) in this solution?

Short answer

The molarity of the Methanol in the solution is 1.85 M.

Step-by-step solution

Find the mass of the solution

First, the total mass of the solution is needed. Given that the density (d) is 0.988 g/mL, and considering 1L of solution (since molarity is moles/Liter), the total mass can be found by converting the volume in mL to L, for 1L, it's 1000mL. Thus, the mass of the solution = d * V = 0.988 g/mL * 1000 mL = 988 g.

Find the mass of Methanol

Next, find the mass of the Methanol (solute). From the problem, we know that the solution is 6.00 % by mass Methanol. So, Methanol will be 6.00 % of the total mass of the solution found in the previous step. Therefore, Mass of Methanol = 6.00/100 * Total mass of solution = 0.0600 * 988 g = 59.28 g.

Find the number of moles

To find molarity, the number of moles is needed. Therefore, the number of moles of the Methanol needs to be calculated using its molar mass. The molar mass of Methanol (CH3OH) is approximately 32.04 g/mole. So, Moles of Methanol = Mass/Molar mass = 59.28 g / 32.04 g/mol = 1.85 moles.

Calculate Molarity

Finally, we can calculate the molarity (M), which is the number of moles per Liter of solution. From earlier steps, we've determined that there are 1.85 moles of Methanol in 1L of solution. So the molarity (M) is just this value M = 1.85 moles / 1 L = 1.85 M.

Key concepts

Molarity Calculation

Molarity is a key concept in chemistry solutions, representing the concentration of a solute in a solution. It measures the number of moles of a solute per liter of solution, which is crucial for quantifying chemical reactions. To calculate molarity, you need to know both the quantity of solute and the volume of the solution.

• Find the number of moles of the solute using its mass and molar mass.
• Determine the total volume of the solution in liters.

The molarity (M) is then calculated using the formula: \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]In our example, Methanol was dissolved in an aqueous solution. We found 1.85 moles of Methanol in 1 liter, making its molarity 1.85 M.

Methanol Solution

Methanol, or wood alcohol, is a simple alcohol with the chemical formula \(\mathrm{CH}_{3} \mathrm{OH}\). It is a key ingredient in the exercise we are solving. Understanding solutions containing Methanol involves acknowledging its properties as a solvent or solute, depending on the context. Methanol is often used in laboratories and industrial applications due to its solvent capabilities and low boiling point. When Methanol dissolves in water, it forms a mixture where the Methanol molecules are evenly distributed throughout the solution. In our problem, the Methanol is the solute, being 6.00% of the total solution's mass. This percentage is essential for calculating concentrations, like molarity, or properties, such as boiling and freezing points.

Density and Concentration

Density plays a significant role in understanding solution concentration. It is defined as the mass of a substance per unit volume and is expressed in \(\mathrm{g}/\mathrm{mL}\). Knowing the density allows us to find the mass of a given volume of solution, which is necessary for concentration calculations.To determine concentration:

• Convert the volume of the solution from liters to milliliters if necessary.
• Multiply the density by this volume to find the mass of the entire solution.

For example, if a solution has a density of 0.988 g/mL, one liter (1000 mL) of the solution weighs 988 grams. Understanding this property helps us accurately measure chemicals and solutions in practical scenarios.

Mass Percent in Solution

Mass percent is a way of expressing a concentration in a solution. It denotes the mass of solute divided by the total mass of the solution, multiplied by 100 to get a percentage. This concept is crucial for understanding how much of each component is present in a solution.The mass percent formula is:\[ \text{Mass percent} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100 \]In our example, a Methanol solution was described as being 6.00% by mass. This means that for every 100 grams of solution, 6 grams are Methanol. Knowing the mass percent can be helpful when translating it into molarity or other concentration measures to fully understand the chemical composition and potential reactivity of a solution.