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Chapter 2: Problem 110

You can make the chromic acid bath commonly used to clean glassware in the lab by dissolving 92 grams of sodium dichromate \(\left(\mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \cdot 2 \mathrm{H}_{2} \mathrm{O}\right)\) in enough wa- ter to give \(458 \mathrm{~mL}\) of solution and then adding \(800 \mathrm{~mL}\) of concentrated sulfuric acid. Calculate the molarity of the \(\mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}\) ion in the solution.

Short Answer

Expert verified
The molarity is 0.245 M.

Step by step solution

01

Calculate moles of sodium dichromate

First, find the molar mass of sodium dichromate dihydrate, \( \mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7 \cdot 2 \mathrm{H}_2 \mathrm{O} \). This involves adding the molar masses of each component: sodium (2 \times 22.99 \text{ g/mol}), chromium (2 \times 51.996 \text{ g/mol}), oxygen (7 \times 16.00 \text{ g/mol}), and water of crystallization (2 \times 18.015 \text{ g/mol}). This results in 298.07 \text{ g/mol}. Now, calculate the moles by dividing the given mass (92 g) by the molar mass: \[ moles = \frac{92 \text{ g}}{298.07 \text{ g/mol}} = 0.3085 \text{ mol} \].
02

Dissolve in solution

The sodium dichromate is dissolved in enough water to make 458 mL of solution, then sulfuric acid is added. Since sulfuric acid doesn't affect the number of moles of \( \mathrm{Cr}_2\mathrm{O}_7^{2-} \) in the solution but just the total volume, focus now on moles of \( \mathrm{Cr}_2\mathrm{O}_7^{2-} \). The moles of sodium dichromate are equal to the moles of \( \mathrm{Cr}_2\mathrm{O}_7^{2-} \), which is 0.3085 mol.
03

Calculate total solution volume in liters

Add the volume of the dichromate solution (458 mL) and the added sulfuric acid (800 mL) to get the total volume of the solution: \[ 458 \text{ mL} + 800 \text{ mL} = 1258 \text{ mL} = 1.258 \text{ L} \].
04

Calculate molarity of \( \mathrm{Cr}_2\mathrm{O}_7^{2-} \) ions

The molarity of an ion in a solution is calculated as \( \frac{\text{moles of solute}}{\text{liters of solution}} \). For \( \mathrm{Cr}_2\mathrm{O}_7^{2-} \): \[ \text{Molarity} = \frac{0.3085 \text{ mol}}{1.258 \text{ L}} = 0.245 \text{ M} \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sodium Dichromate
Sodium dichromate, a chemical compound with the formula \( \text{Na}_2\text{Cr}_2\text{O}_7 \cdot 2\text{H}_2\text{O} \), is often used in laboratories for its oxidative properties. It appears as a bright orange to red crystalline solid and is valuable for various applications, including glassware cleaning. This compound contains sodium, chromium, and oxygen atoms along with water molecules as seen in its chemical structure.
Sodium dichromate is utilized frequently because it dissociates in water to provide chromate ions which are effective in oxidizing organic substances.
  • It is hazardous and should be handled with care since it is toxic and a potential carcinogen.
  • Always make sure to work with it in a well-ventilated area and use personal protective equipment.
Chromic Acid Bath
A chromic acid bath is a solution primarily used in scientific settings for cleaning glassware and removing organic residues. The bath is made by mixing sodium dichromate with sulfuric acid. This combination creates an extremely powerful cleaning solution that helps ensure glassware is free from contaminants.
Using a chromic acid bath is beneficial because:
  • It provides thorough cleaning that many other solutions can't achieve.
  • The oxidizing nature of chromic acid effectively breaks down organic molecules.
However, due to its strength and corrosive nature, it's crucial to strictly follow safety protocols and manage waste properly.
Molar Mass Calculation
Molar mass is the weight of one mole of a chemical compound. To calculate the molar mass of a compound like sodium dichromate dihydrate \( \text{Na}_2\text{Cr}_2\text{O}_7 \cdot 2\text{H}_2\text{O} \), you must sum the atomic masses of its constituent elements.
Here's a breakdown:
  • Sodium (Na): 2 atoms with an atomic mass of 22.99 g/mol each.
  • Chromium (Cr): 2 atoms with an atomic mass of 51.996 g/mol each.
  • Oxygen (O): 7 atoms with an atomic mass of 16.00 g/mol each.
  • Water of crystallization: 2 molecules with an atomic mass of 18.015 g/mol each.
When you add these values, the total molar mass of sodium dichromate dihydrate comes to 298.07 g/mol. This fundamental calculation is essential for determining how many moles of a substance you have, especially when preparing solutions.
Aqueous Solution Preparation
The preparation of an aqueous solution involves dissolving a solute (in this case sodium dichromate) in a solvent, which is water, to form a stable solution.
When preparing an aqueous solution, it's essential to follow the proper steps:
  • Begin by accurately weighing out the solute necessary for your desired concentration.
  • Then dissolve this solute in a specific volume of solvent. Initially, add a bit of water to dissolve the solute properly before bringing the solution up to the final desired volume.
In the context of this exercise, 92 grams of sodium dichromate are dissolved to make 458 mL of solution before adding sulfuric acid. The accuracy in solution preparation affects the final molarity, which measures the concentration of ions present, making it a critical step in laboratory procedures.

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Most popular questions from this chapter

A 2.50 -gram sample of bronze was dissolved in sulfuric acid. The copper in the alloy reacted with sulfuric acid as follows. $$ \begin{aligned} \mathrm{Cu}(s)+& 2 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \\ & \longrightarrow \mathrm{CuSO}_{4}(a q)+\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned} $$ The \(\mathrm{CuSO}_{4}\) formed in the reaction was mixed with \(\mathrm{KI}\) to form CuI. $$ \begin{aligned} 2 \mathrm{CuSO}_{4}(a q) &+5 \mathrm{I}^{-}(a q) \\ \longrightarrow & 2 \mathrm{CuI}(s)+\mathrm{I}_{3}^{-}(a q)+2 \mathrm{SO}_{4}^{2-}(a q) \end{aligned} $$ The \(\mathrm{I}_{3}^{-}\) ion formed in this reaction was then titrated with \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}\). $$ \mathrm{I}_{3}^{-}(a q)+2 \mathrm{~S}_{2} \mathrm{O}_{3}^{2-}(a q) \longrightarrow 3 \mathrm{I}^{-}(a q)+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}(a q) $$ Calculate the percentage by mass of copper in the original sample if \(31.5 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{S}_{2} \mathrm{O}_{3}^{2-}\) were consumed in the titration.

Calculate the mass of hydrogen chloride that can be produced from 10.0 grams of hydrogen and 10.0 grams of chlorine. $$ \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g) $$ What would have to be done to increase the amount of hydrogen chloride produced in the reaction?

Nitrogen reacts with red-hot magnesium to form magnesium nitride, $$ 3 \mathrm{Mg}(s)+\mathrm{N}_{2}(g) \longrightarrow \mathrm{Mg}_{3} \mathrm{~N}_{2}(s) $$ which reacts with water to form magnesium hydroxide and ammonia. $$ \begin{array}{r} \mathrm{Mg}_{3} \mathrm{~N}_{2}(s)+6 \mathrm{H}_{2} \mathrm{O} \longrightarrow 3 \mathrm{Mg}(\mathrm{OH})_{2}(a q) \\ +2 \mathrm{NH}_{3}(a q) \end{array} $$ Calculate the number of grams of magnesium that would be needed to prepare 15.0 grams of ammonia.

$$ \text { What is the mass in grams of } 4.35 \times 10^{6} \text { atoms of }{ }^{12} \mathrm{C} ? $$

Calculate the molarity of an acetic acid \(\left(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\right)\) solution if \(34.57 \mathrm{~mL}\) of the solution are needed to react with \(25.19 \mathrm{~mL}\) of \(0.1025 \mathrm{M}\) sodium hydroxide. $$ \begin{array}{l} \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(a q)+\mathrm{NaOH}(a q) \\ \longrightarrow \mathrm{Na}^{+}(a q)+\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \end{array} $$
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