Question

How many milliliters of \(0.265 \mathrm{M} \mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) are needed to supply \(14.3 \mathrm{~g} \mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} ?\)

Short answer

657.7 mL of 0.265 M NaC2H3O2 are needed to supply 14.3 g NaC2H3O2.

Step-by-step solution

Determine the Molar Mass of NaC2H3O2

To find how many milliliters of the solution are needed, we first need to calculate the molar mass of sodium acetate (NaC2H3O2). By using the periodic table, add the atomic masses of sodium (Na), carbon (C), hydrogen (H), and oxygen (O) in the chemical formula: Molar mass of NaC2H3O2 = (1 × 22.99) + (2 × 12.01) + (3 × 1.008) + (2 × 16.00) = 22.99 + 24.02 + 3.024 + 32.00 = 82.034 g/mol.

Convert Grams to Moles

Next, convert the given mass of sodium acetate to moles using the molar mass from Step 1: Number of moles = Mass given / Molar mass = 14.3 g / 82.034 g/mol = 0.1743 moles.

Calculate the Volume needed

Using the molarity formula (Molarity = Moles of solute / Volume of solution in liters), rearrange it to calculate the volume: Volume (L) = Moles of solute / Molarity. Volume (L) = 0.1743 moles / 0.265 M = 0.6577 L. Then convert the volume from liters to milliliters by multiplying by 1000: Volume (mL) = 0.6577 L × 1000 mL/L = 657.7 mL.

Key concepts

Molar Mass Calculation

Understanding the molar mass of a compound is essential to many aspects of chemistry. It's the combined weight of all atoms in a molecule, expressed in grams per mole (g/mol). Having this knowledge allows chemists to relate the mass of a substance to the number of its molecules or atoms, a cornerstone of stoichiometry.

For instance, sodium acetate (NaC2H3O2) has its molar mass determined by summing the atomic masses of all the atoms in a single molecule. If you consult the periodic table, each atom's mass is given, usually in atomic mass units (amu) or daltons (Da). These are equivalent to grams per mole for our purposes.

To calculate the molar mass, multiply the atomic mass of each element by the number of times that element appears in the formula and add all these values together. The result will give you the compound's molar mass in grams per mole, which is crucial for subsequent steps such as converting grams to moles or determining the concentrations in solutions.

Converting Grams to Moles

When you're facing a problem that involves measuring the amount of a substance, often you will be given its mass in grams and will need to convert this to moles to proceed with calculations in a chemical context. This conversion is facilitated by using the compound's molar mass.

The formula is straightforward: \[\text{Number of moles} = \frac{\text{Mass given (in grams)}}{\text{Molar mass (g/mol)}}\]
For an example, if we have 14.3 grams of sodium acetate and its molar mass is 82.034 g/mol, using the formula gives us the number of moles. This step is pivotal because reactions in chemistry are often discussed in terms of moles, which provides a common currency for discussing the amounts of substances involved.

Molarity Formula

The concentration of a solution is commonly expressed as molarity, denoted as 'M'. Molarity is defined as the number of moles of a solute present in one liter of solution. It shows how concentrated the solution is. To find the molarity, you can use the formula: \[\text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters (L)}}\]

When you're given a molarity and a number of moles, and you need to find the volume of solution, rearrange the formula to solve for the volume: \[\text{Volume (L)} = \frac{\text{Moles of solute}}{\text{Molarity (M)}}\]
This becomes particularly useful when preparing solutions in a lab setting or when you’re trying to determine how much of a stock solution you need for a given experiment. Converting molarity into a usable volume is a common task in chemistry that bridges theoretical concepts with practical applications.

Volume Calculation

In chemistry, it’s often necessary to calculate the volume of a solution required to have a certain amount of solute. This process can vary in complexity depending on the units involved, and you may need to perform conversions to achieve your result.

For instance, after determining the volume in liters using the molarity formula, as seen in our sodium acetate example, you might need the answer in milliliters (mL). Since there are 1000 milliliters in a liter, you would multiply the volume in liters by 1000 to get your final answer in milliliters: \[\text{Volume (mL)} = \text{Volume (L)} \times 1000 \text{ mL/L}\]
Situations like these are common in laboratory work where reagents are often measured in milliliters. Thus, mastering volume calculations allows chemists to accurately prepare solutions, which is vital for experimental success.