Question

Calculate the volume in \(\mathrm{mL}\) of a solution required to provide the following: (a) \(2.14 \mathrm{~g}\) of sodium chloride from a \(0.270 \mathrm{M}\) solution, (b) \(4.30 \mathrm{~g}\) of ethanol from a \(1.50 M\) solution, (c) 0.85 g of acetic acid ( \(\left.\mathrm{CH}_{3} \mathrm{COOH}\right)\) from a \(0.30 \mathrm{M}\) solution.

Short answer

The volumes required for each solution are as follows: (a) 135.5 mL of the sodium chloride solution, (b) 62.2 mL of the ethanol solution, and (c) 47.2 mL of the acetic acid solution.

Step-by-step solution

Conversion into Moles

Firstly, we need to convert the given masses into moles. The number of moles (n) can be found by dividing the given mass (m) of each substance by its molar mass (Mm). For (a) sodium chloride (NaCl), the molar mass is approximately 58.44 g/mol. So, \(n_{NaCl} = \frac{m_{NaCl}}{Mm_{NaCl}} = \frac{2.14 g}{58.44 g/mol} = 0.0366 mol\)For (b) ethanol (C2H5OH), the molar mass is approximately 46.07 g/mol. So, \(n_{Ethanol} = \frac{m_{Ethanol}}{Mm_{Ethanol}} = \frac{4.30 g}{46.07 g/mol} = 0.0933 mol\)For (c) acetic acid (CH3COOH), the molar mass is approximately 60.05 g/mol. So, \(n_{Acetic Acid} = \frac{m_{Acetic Acid}}{Mm_{Acetic Acid}} = \frac{0.85 g}{60.05 g/mol} = 0.0142 mol\)

Applying Molarity Formula

Secondly, we use the molarity formula to calculate the volume required for each solution. The molarity formula can be rearranged to find the volume (V) as follows: \(V=\frac{n}{M}\), where V is the volume in liters. To get the volume in milliliters (mL), we multiply by 1000. For (a) the sodium chloride solution: \(V_{NaCl} = \frac{n_{NaCl}}{M_{NaCl}} * 1000 = \frac{0.0366 mol}{0.270 M} * 1000 = 135.5 mL\)For (b) the ethanol solution: \(V_{Ethanol} = \frac{n_{Ethanol}}{M_{Ethanol}} * 1000 = \frac{0.0933 mol}{1.50 M} * 1000 = 62.2 mL\)For (c) the acetic acid solution: \(V_{Acetic Acid} = \frac{n_{Acetic Acid}}{M_{Acetic Acid}} * 1000 = \frac{0.0142 mol}{0.30 M} * 1000 = 47.2 mL\)

Key concepts

Molarity Calculations

Molarity is a fundamental concept in chemistry that measures the concentration of a solute in a solution. It is expressed as the number of moles of solute per liter of solution, represented by the formula:
\[ M = \frac{n}{V} \]
where \( M \) is the molarity, \( n \) is the number of moles of the solute, and \( V \) is the volume of the solution in liters. Molarity is a convenient way to express concentration because it directly relates the amount of substance to the volume of the solution.

• To calculate molarity, you first need to know the number of moles of the solute.
• Then, determine the volume of the entire solution in liters.
• Finally, use the formula to find the molarity.

Once determined, the molarity can help calculate other properties of the solution, such as the required volume for a specific amount of solute. This is particularly useful in laboratory settings where precise measurements are required.

Mass to Moles Conversion

Understanding how to convert mass to moles is a key skill in chemistry. This conversion allows us to relate the mass of a chemical substance to the number of molecules or atoms it contains. The basic formula is:
\[ n = \frac{m}{M_m} \]
where \( n \) is the number of moles, \( m \) is the mass of the substance, and \( M_m \) is the molar mass.

• The molar mass of a substance (typically in grams per mole) is the mass of one mole of its atoms, molecules, or formula units.
• You can usually find this value on the periodic table or by adding the atomic masses of the elements in a compound.

For example, if you're working with ethanol (C\(_2\)H\(_5\)OH), the molar mass is approximately 46.07 g/mol. If you have 4.30 g of ethanol, converting to moles requires dividing the mass by the molar mass: \( \frac{4.30}{46.07} \approx 0.0933 \) moles.
This conversion step is crucial for accurately applying molarity formulas and ultimately determining how much of a solution you will need.

Volume Calculation in Chemistry

Calculating the volume of a solution needed to achieve a desired concentration is common in chemistry. Once you have the molarity and number of moles, you can find the required volume using:
\[ V = \frac{n}{M} \]
where \( V \) is the volume in liters.

• First, convert the amount of solute into moles, which we previously covered.
• Use the rearranged molarity formula to solve for volume.
• Don't forget to convert the volume from liters to milliliters by multiplying by 1000 for use in most laboratory settings.

For instance, to find out how much volume is needed for a sodium chloride (NaCl) solution, you would rearrange the formula: \( V = \frac{0.0366}{0.270} \cdot 1000 = 135.5 \) mL. Here the given number of moles was 0.0366 and the molarity is 0.270 M. This calculated volume is what would be prepared to provide the exact concentration needed for the experiment.