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A \(2.500\) -g sample of a mixture of sodium carbonate and sodium chloride is dissolved in \(25.00 \mathrm{~mL}\) of \(0.798 \mathrm{M} \mathrm{HCl}\). Some acid remains after the treatment of the sample. a. Write the net ionic equation for the complete reaction of sodium carbonate with hydrochloric acid. b. If \(28.7 \mathrm{~mL}\) of \(0.108 M \mathrm{NaOH}\) were required to titrate the excess hydrochloric acid, how many moles of sodium carbonate were present in the original sample? C. What is the percent composition of the original sample?

Short Answer

Expert verified
\( \text{CO}_3^{2-} + 2 \text{H}^+ \rightarrow \text{H}_2\text{O} + \text{CO}_2 \); 0.008425 mol \( \text{Na}_2\text{CO}_3 \); 35.68\% \( \text{Na}_2\text{CO}_3 \), 64.32\% \( \text{NaCl} \)

Step by step solution

01

Write the Net Ionic Equation

To find the net ionic equation for the reaction of sodium carbonate (\( \text{Na}_2\text{CO}_3 \)) with hydrochloric acid (\( \text{HCl} \)), we start with the full reaction: \[ \text{Na}_2\text{CO}_3 (aq) + 2 \text{HCl} (aq) \rightarrow 2 \text{NaCl} (aq) + \text{H}_2\text{O} (l) + \text{CO}_2 (g) \] The net ionic equation involves only the species that undergo a change: \[ \text{CO}_3^{2-} (aq) + 2 \text{H}^+ (aq) \rightarrow \text{H}_2\text{O} (l) + \text{CO}_2 (g) \]
02

Calculate Moles of HCl Used

We first find the moles of \(\text{HCl}\) initially present in the solution with a molarity of \(0.798 \text{M}\) in \(25.00 \text{mL}\): \[ \text{n}_\text{HCl} = 0.798 \text{mol/L} \times 0.02500 \text{L} = 0.01995 \text{mol} \]
03

Calculate Moles of NaOH Used for Titration

Determine the moles of \(\text{NaOH}\) used in the titration with \(0.108 \text{M}\) in \(28.7 \text{mL}\): \[ \text{n}_\text{NaOH} = 0.108 \text{mol/L} \times 0.0287 \text{L} = 0.003100 \text{mol} \]
04

Determine Moles of Excess HCl

Since \(\text{NaOH}\) neutralizes \(\text{HCl}\) at a 1:1 ratio, moles of excess \(\text{HCl}\) = moles of \(\text{NaOH}\): \[ \text{n}_\text{HCl, excess} = 0.003100 \text{mol} \]
05

Calculate Moles of HCl Reacted with Sodium Carbonate

Subtract the moles of excess \(\text{HCl}\) from the total moles to find moles reacting with \(\text{Na}_2\text{CO}_3\): \[ \text{n}_\text{HCl, reacted} = 0.01995 \text{mol} - 0.003100 \text{mol} = 0.01685 \text{mol} \] Since \(2\text{HCl}\) react with each \( \text{Na}_2\text{CO}_3\) (from balanced equation), the moles of \( \text{Na}_2\text{CO}_3 \) is \(\frac{0.01685}{2} = 0.008425 \text{mol} \).
06

Calculate Mass of Sodium Carbonate

Using the molar mass of sodium carbonate (\(\text{Na}_2\text{CO}_3\) = 105.99 g/mol): \[ \text{mass } \text{Na}_2\text{CO}_3 = 0.008425 \text{mol} \times 105.99 \text{g/mol} = 0.892 \text{g} \]
07

Determine Percent Composition

The original mixture weighed \(2.500 \text{g}\). Hence, the percent composition is calculated as: \[ \text{percent } \text{Na}_2\text{CO}_3 = \left( \frac{0.892}{2.500} \right) \times 100 = 35.68\% \] The percent of \(\text{NaCl}\) would be \(100\% - 35.68\% = 64.32\%\).

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Key Concepts

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

Net Ionic Equation
In chemistry, a net ionic equation is a way to express only the substances actively involved in a chemical reaction. This is useful for simplifying equations because it focuses on the *actual* chemical change. Net ionic equations omit spectator ions, which do not participate directly in the reaction.
For the reaction of sodium carbonate (\text{Na}_2\text{CO}_3) with hydrochloric acid (\text{HCl}), the overall equation is:\[\text{Na}_2\text{CO}_3 (aq) + 2 \text{HCl} (aq) \rightarrow 2 \text{NaCl} (aq) + \text{H}_2\text{O} (l) + \text{CO}_2 (g)\]However, simplifying to the net ionic equation, we remove the sodium and chloride ions, as they are just present but not part of the reaction change:
\[\text{CO}_3^{2-} (aq) + 2 \text{H}^+ (aq) \rightarrow \text{H}_2\text{O} (l) + \text{CO}_2 (g)\]
  • "\text{CO}_3^{2-}": Carbonate ion from sodium carbonate.
  • "\text{H}^+": Hydrogen ion from hydrochloric acid.
  • "\text{H}_2\text{O}": Water, produced from reaction.
  • "\text{CO}_2": Carbon dioxide, a gaseous product.
Notice how the sodium and chloride ions are not included in the net ionic equation? This underlines the focus on reacting particles.
Chemical Reaction
A chemical reaction involves transforming reactants into products. During a reaction, bonds within molecules are broken and formed, resulting in new substances. Chemical reactions are usually characterized by changes such as formation of gas, color change, or temperature change.
To further illustrate chemical reactions, let's consider our example where sodium carbonate (\text{Na}_2\text{CO}_3) reacts with hydrochloric acid (\text{HCl}).
When these two compounds react, they produce sodium chloride (\text{NaCl}), water (\text{H}_2\text{O}), and carbon dioxide (\text{CO}_2). The reaction itself exemplifies a double displacement reaction followed by the decomposition of carbonic acid into water and carbon dioxide. This is seen in:
\[\text{Na}_2\text{CO}_3 (aq) + 2 \text{HCl} (aq) \rightarrow 2 \text{NaCl} (aq) + \text{H}_2\text{O} (l) + \text{CO}_2 (g)\]Here:
  • \text{Na}_2\text{CO}_3: Breaks into sodium ions and carbonate ions.
  • \text{HCl}: Provides hydrogen ions which combine with carbonate to form water and carbon dioxide.
  • \text{NaCl}: Resulting salt from displaced ions.
Remember, observing these kinds of reactions can offer real-world insights, such as understanding how carbon dioxide is released, similar to biological systems.
Molarity
Molarity is a measurement of concentration, describing how many moles of a substance are present per liter of solution. It's commonly used to express the concentration of a solute in a solution, helping chemists standardize how strong or weak a solution is.
The formula for molarity (M) is given by:
\[M = \frac{n}{V}\]where
  • \( n \): Amount of solute in moles
  • \( V \): Volume of solution in liters
In our exercise, hydrochloric acid was 0.798 M, meaning 0.798 moles of HCl exist per liter. This concentration allowed us to calculate precisely how much acid was reacting or in excess. Similarly, during the titration step, knowing the molarity of NaOH (0.108 M) made it easier to compute the exact moles of NaOH that reacted.
The use of molarity in calculations such as determining leftover amounts after a reaction, or adjusting the concentration of solutions, is foundational in laboratory work, enabling accurate compositions and reactions.
Percent Composition
Percent composition determines what portion of a mixture or compound is attributable to each component. It is expressed on a percentage basis and hence gives clarity on how much each part contributes to the whole.
In chemical analysis, finding the percent composition is crucial for understanding mixtures. In our exercise, the sample consisted of a mixture of sodium carbonate and sodium chloride.
After executing all calculations to find the mass of sodium carbonate, you use the formula:
\[\text{Percent Composition} = \left( \frac{\text{Mass of Component}}{\text{Total Mass of Mixture}} \right) \times 100\]For sodium carbonate in our original mixture, it turned out to be 35.68%. This was determined by dividing its mass (0.892 g) by the total sample mass (2.500 g), then multiplying by 100.
  • Allows determination of each component's contribution.
  • It's essential for creating desired mixture properties.
  • Can highlight purity or concentration of a compound.
Calculating percent composition is especially useful in scientific research, industry applications, and even in cooking to ensure correctness of ingredient ratios.

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Most popular questions from this chapter

Coal and other fossil fuels usually contain sulfur compounds that produce sulfur dioxide, \(\mathrm{SO}_{2}\), when burned. One possible way to remove the sulfur dioxide is to pass the combustion gases into a tower packed with calcium oxide, \(\mathrm{CaO}\). Write the equation for the reaction. Identify each reactant as either a Lewis acid or a Lewis base. Explain how you arrived at your answer.

For each of the following pairs, give the stronger acid. Explain your answer. a. \(\mathrm{H}_{2} \mathrm{~S}, \mathrm{HS}\) b. \(\mathrm{H}_{2} \mathrm{SO}_{3}, \mathrm{H}_{2} \mathrm{SeO}_{3}\) c. \(\mathrm{HBr}, \mathrm{H}_{2} \mathrm{Se}\) d. \(\mathrm{HIO}_{4}, \mathrm{HIO}_{3}\) e. \(\mathrm{H}_{2} \mathrm{~S}, \mathrm{H}_{2} \mathrm{O}\)

You make a solution by dissolving \(0.0010\) mol of \(\mathrm{HCl}\) in enough water to make \(1.0 \mathrm{~L}\) of solution. a. Write the chemical equation for the reaction of \(\mathrm{HCl}(a q)\) and water. b. Without performing calculations, give a rough estimate of the \(\mathrm{pH}\) of the \(\mathrm{HCl}\) solution. Justify your answer. c. Calculate the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration and the \(\mathrm{pH}\) of the solution. d. Is there any concentration of the base \(\mathrm{OH}^{-}\) present in this solution of \(\mathrm{HCl}(a q) ?\) If so, where did it come from? e. If you increase the OH \(^{-}\) concentration of the solution by adding \(\mathrm{NaOH}\), does the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration change? If you think it does, explain why this change occurs and whether the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration increases or decreases. f. If you were to measure the \(\mathrm{pH}\) of 10 drops of the original HCl solution, would you expect it to be different from the pH of the entire sample? Explain. g. Explain how two different volumes of your original \(\mathrm{HCl}\) solution can have the same \(\mathrm{pH}\) yet contain different moles of \(\mathrm{H}_{3} \mathrm{O}^{+}\) h. If \(1.0 \mathrm{~L}\) of pure water were added to the \(\mathrm{HCl}\) solution, would this have any impact on the \(\mathrm{pH}\) ? Explain.

For the following reactions, label each species as an acid or a base. Indicate the species that are conjugates of one another. a. \(\mathrm{HSO}_{4}^{-}+\mathrm{NH}_{3} \rightleftharpoons \mathrm{SO}_{4}^{2-}+\mathrm{NH}_{4}^{+}\) b. \(\mathrm{HPO}_{4}^{2-}+\mathrm{NH}_{4}^{+} \rightleftharpoons \mathrm{H}_{2} \mathrm{PO}_{4}^{-}+\mathrm{NH}_{3}\) c. \(\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{OH}^{2+}+\mathrm{H}_{3} \mathrm{O}^{+}\) d. \(\mathrm{SO}_{3}^{2-}+\mathrm{NH}_{4}^{+} \rightleftharpoons \mathrm{HSO}_{3}^{-}+\mathrm{NH}_{3}\)

Write the balanced reaction of hydroxide ion with hydrofluoric acid, HF, to form fluoride ion and water. Identify each species as either an acid or a base.

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