Problem 62 - Chemistry: The Central Science

Question

(a) Calculate the molarity of a solution made by dissolving \(12.5\) grams of \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) in enough water to form exactly \(750 \mathrm{~mL}\) of solution. (b) How many moles of \(\mathrm{KBr}\) are present in \(150 \mathrm{~mL}\) of a \(0.112 \mathrm{M}\) solution? (c) How many milliliters of \(6.1 \mathrm{M} \mathrm{HCl}\) solution are needed to obtain \(0.150 \mathrm{~mol}\) of \(\mathrm{HCl}\) ?

Step-by-Step Solution

Answer

(a) The molarity of the Na2CrO4 solution is 0.0636 M. (b) There are 0.0168 moles of KBr in the 150 mL solution. (c) It will require 24.6 mL of the 6.1 M HCl solution to obtain 0.150 mol of HCl.

Step 1: Part (a): Calculate the molarity of the Na2CrO4 solution

To solve this, we will first convert the mass of Na2CrO4 to moles, and then use the volume of the solution to compute the molarity. Step 1: Find the molar mass of Na2CrO4 Molar mass of Na2CrO4 = 2 × (Molar mass of Na) + (Molar mass of Cr) + 4 × (Molar mass of O) Molar mass of Na2CrO4 = 2 × (22.99 g/mol) + (51.996 g/mol) + 4 × (16.00 g/mol) Molar mass of Na2CrO4 = 261.966 g/mol Step 2: Convert grams to moles Moles of Na2CrO4 = (12.5 g) / (261.966 g/mol) = 0.0477 mol Step 3: Convert milliliters to liters Volume of the solution in liters = 750 mL × (1 L / 1000 mL) = 0.75 L Step 4: Calculate the molarity Molarity (M) = Moles of solute / Volume of solution M = 0.0477 mol / 0.75 L = 0.0636 M So, the molarity of the Na2CrO4 solution is 0.0636 M.

Step 2: Part (b): Calculate the moles of KBr

To find the moles of KBr in the solution, we will use the given molarity and volume of the solution. Step 1: Convert milliliters to liters Volume of the solution in liters = 150 mL × (1 L / 1000 mL) = 0.15 L Step 2: Calculate the moles of KBr using the molarity Moles of KBr = Molarity × Volume of solution Moles of KBr = 0.112 M × 0.15 L = 0.0168 mol There are 0.0168 moles of KBr in the 150 mL solution.

Step 3: Part (c): Find the volume of the 6.1 M HCl solution

To find the volume of the HCl solution required to obtain 0.150 mol of HCl, we will use the given molarity and moles of the solute. Step 1: Use moles and molarity to find the volume Volume of solution in liters = Moles of solute / Molarity Volume = 0.150 mol / 6.1 M = 0.0246 L Step 2: Convert liters to milliliters Volume of solution in milliliters = 0.0246 L × (1000 mL / 1 L) = 24.6 mL It will require 24.6 mL of the 6.1 M HCl solution to obtain 0.150 mol of HCl.

Key Concepts

Solution Concentration

When we talk about solution concentration, we are discussing how much of a substance (the solute) is present in a certain volume of solution. A common unit to express this is molarity (M), which is defined as the number of moles of solute per liter of solution.

• Molarity = Moles of solute / Volume of solution in liters

Molarity is a key concept in chemistry because it helps us understand how substances interact in a solution. For instance, when given a problem to find the molarity of a solution, one must first determine the number of moles of the solute and the volume of the solution. Only then can you calculate the molarity by dividing the moles by the volume expressed in liters.
In practice, if you have a solution where 0.0477 moles of a solute are dissolved in 0.75 liters, the molarity would be computed as follows: 0.0477 mol divided by 0.75 L, resulting in a molarity of 0.0636 M. This example illustrates how concentration is an intrinsic property of a solution and is vital for chemical calculations.

Chemical Calculations

Chemical calculations play an essential role in accurately predicting the quantities involved in chemical reactions and processes. They ensure that you can calculate the exact amount of substances needed or produced.
The skill of converting units and manipulating formulas is fundamental here. For instance, when converting a volume from milliliters to liters, you divide the milliliters by 1000 because there are 1000 milliliters in one liter.
Similarly, when dealing with moles and volumes in chemical calculations, it's crucial to arrange the known values with the right formula. For instance, to find the volume of a solution required to reach a specific number of moles, we use the formula:

• Volume (in liters) = Moles of solute / Molarity

These calculations allow chemists to mix reagents precisely and can dictate how reactions proceed in laboratory settings.

Moles and Molar Mass

Understanding moles and molar mass is fundamental in chemistry as they bridge the gap between macroscopic amounts of substances and their molecular scale.
The mole is a unit for counting particles, based on Avogadro's number, which is approximately 6.022 × 10²³ particles per mole. Molar mass, meanwhile, is the mass of one mole of a substance, typically given in grams per mole (g/mol). Each element has its own molar mass, found on the periodic table. For compounds, like \( ext{Na}_2 ext{CrO}_4\), the molar mass is calculated by summing the molar masses of each constituent element multiplied by their respective frequencies in the formula.
For example, the molar mass of \( ext{Na}_2 ext{CrO}_4\) is found by adding twice the molar mass of sodium, the molar mass of chromium, and four times the molar mass of oxygen. The correct calculation ensures that when you convert grams to moles, the values reflect the actual number of molecules present, which is crucial for chemical reactions and solutions preparation.