/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 133 Calculate the molarity of a sodi... [FREE SOLUTION] | 91Ó°ÊÓ

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Calculate the molarity of a sodium hydroxide solution if \(10.42 \mathrm{~mL}\) of this solution are needed to react with \(25.00 \mathrm{~mL}\) of \(0.2043 \mathrm{M}\) oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) $$ \begin{aligned} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q)+& 2 \mathrm{NaOH}(a q) \\ & \longrightarrow \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned} $$

Short Answer

Expert verified
The molarity of the NaOH solution is approximately 0.9809 M.

Step by step solution

01

Write the Balanced Chemical Equation

The chemical equation for the reaction between oxalic acid \( H_2C_2O_4 \) and sodium hydroxide \( NaOH \) is: \[ \mathrm{H}_2\mathrm{C}_2\mathrm{O}_4(aq) + 2\mathrm{NaOH}(aq) \rightarrow \mathrm{Na}_2\mathrm{C}_2\mathrm{O}_4(aq) + 2\mathrm{H}_2\mathrm{O}(l) \] This tells us that 1 mole of oxalic acid reacts with 2 moles of sodium hydroxide.
02

Calculate Moles of Oxalic Acid

The molarity of the oxalic acid is given as \(0.2043\, M\), and the volume is \(25.00\, \mathrm{mL}\). First, convert the volume to liters: \[ 25.00\, \mathrm{mL} = 0.02500\, \mathrm{L} \]Then, calculate the moles of oxalic acid using the formula:\[\text{moles} = \text{molarity} \times \text{volume (L)}\]\[\text{moles of } H_2C_2O_4 = 0.2043\, M \times 0.02500\, L = 0.0051075\, \text{moles}\]
03

Use Stoichiometry to Find Moles of NaOH

According to the balanced equation, 1 mole of oxalic acid reacts with 2 moles of NaOH. Therefore, the moles of NaOH required are:\[\text{moles of NaOH} = 2 \times 0.0051075\, \text{moles of } H_2C_2O_4 = 0.010215\, \text{moles}\]
04

Calculate the Molarity of NaOH

The volume of the NaOH solution used is \(10.42\, \mathrm{mL}\), which is \(0.01042\, \mathrm{L}\). Use the formula for molarity:\[\text{Molarity} = \frac{\text{moles}}{\text{volume (L)}}\]\[\text{Molarity of NaOH} = \frac{0.010215\, \text{moles}}{0.01042\, L} \approx 0.9809\, M\]

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Key Concepts

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

Stoichiometry
Stoichiometry is a fundamental concept in chemistry that involves the calculation of reactants and products in chemical reactions. It is based on the balanced equations that represent these reactions. In the context of our exercise, stoichiometry helps us determine the exact amounts needed for substances to completely react without any leftover.The balanced chemical equation given in the exercise is:\[\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}(aq) + 2\mathrm{NaOH}(aq) \rightarrow \mathrm{Na}_{2}\mathrm{C}_{2}\mathrm{O}_{4}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l)\]Here, it clearly shows the stoichiometric coefficients: 1 mole of oxalic acid reacts with 2 moles of sodium hydroxide (NaOH). This relationship is key to determining how much of each substance is needed for a reaction or how much product you can expect to obtain.
  • The coefficients provide a ratio, which is crucial for calculations.
  • Each substance in the reaction is measured in moles, a unit used to express amounts at a molecular level.
  • By using stoichiometry, you can scale up from one part of the equation to others to find out the necessary or resulting quantities involved in chemical reactions.
Chemical Reactions
Chemical reactions are processes where substances, known as reactants, are transformed into different substances, called products. This transformation happens through the breaking and forming of bonds between atoms. In our example, we are looking at a neutralization reaction - a common type of reaction.This particular reaction involves oxalic acid (\(\mathrm{H}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\)) and sodium hydroxide (NaOH), which react to form sodium oxalate (\(\mathrm{Na}_{2}\mathrm{C}_{2}\mathrm{O}_{4}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)).Characteristics of this chemical reaction include:
  • Reactants and products are expressed in aqueous (aq) or liquid (l) states.
  • Acids and bases react to form a salt and water, which is typical for neutralization reactions.
  • The conservation of matter principle applies; atoms are neither created nor destroyed, only rearranged.
Understanding the nature of the reaction informs how stoichiometry is applied, by dictating the relationships and proportions of substances involved.
Solution Concentration
Solution concentration tells us how much solute is present compared to the solvent within a mixture. The most common units for concentration are molarity (M), which quantifies the number of moles of solute per liter of solution.In this example, we need to find the molarity of the sodium hydroxide solution, which required reactions with a known concentration of oxalic acid.Here's how you tackle molarity calculations:1. **Identify Known Variables:** In our problem, we start with the concentration and volume of oxalic acid (0.2043 M and 25.00 mL). - We convert the volume of oxalic acid to liters to ensure units are consistent for use in the molarity formula.2. **Calculate Moles:** Use the molarity formula to calculate moles of the solute (here, oxalic acid). - Formula: \[\text{moles of oxalic acid} = \text{molarity} \times \text{volume (L)}\]3. **Determine Equivalent Reactant Moles:** Use stoichiometry to determine how many moles of NaOH correspond to the moles of oxalic acid.4. **Calculate Unknown Molarity:** Now apply the moles found to calculate the molarity of NaOH: - Adjust for the volume of NaOH used (10.42 mL converted to liters). - Formula: \[\text{Molarity of NaOH} = \frac{\text{moles of NaOH}}{\text{volume (L)}}\]This step-by-step approach helps us use known variables to solve for unknown concentrations, ensuring accurate chemical formulations and effective problem-solving skills.

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Most popular questions from this chapter

A molecule containing only nitrogen and oxygen conains \(36.8 \% \mathrm{~N}\) by mass. (a) How many grams of \(\mathrm{N}\) would be found in a 100 gram sample of the compound? How many grams of \(\mathrm{O}\) would be found in the same sample? (b) How many moles of \(\mathrm{N}\) would be found in a 100 -gram sample of the compound? How many moles of \(\mathrm{O}\) would be found in the same sample? (c) What is the ratio of the number of moles of \(\mathrm{O}\) to the number of moles of \(\mathrm{N} ?\) (d) What is the empirical formula of the compound?

Calculate the molecular weight of the following compounds. (a) chromium hexacarbonyl, \(\mathrm{Cr}(\mathrm{CO})_{6}\) (b) iron(III) nitrate, \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) (c) potassium dichromate, \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) (d) calcium phosphate, \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Assume that two experiments are performed on the following chemical reaction: $$ \begin{array}{lccl} 2 \mathrm{Br}^{-}(a q) & \+ & \mathrm{Cl}_{2}(a q) & \longrightarrow & \mathrm{Br}_{2}(a q)+ & 2 \mathrm{Cl}^{-}(a q) \\ \text { Colorless } & \text { Colorless } & \text { Red } & \text { Colorless } \end{array} $$ \- Experiment \(1: 100 \mathrm{~mL}\) of a \(0.0100 \mathrm{M}\) solution of \(\mathrm{Br}^{-}\) are added to \(100 \mathrm{~mL}\) of a \(0.0200 \mathrm{M}\) solution of \(\mathrm{Cl}_{2}\) \- Experiment \(2: 100 \mathrm{~mL}\) of a \(0.0100 \mathrm{M}\) solution of \(\mathrm{Br}^{-}\) are added to \(100 \mathrm{~mL}\) of a \(0.0500 \mathrm{M}\) solution of \(\mathrm{Cl}_{2}\) If the reaction between aqueous solutions of the \(\mathrm{Br}^{-}\) ion and \(\mathrm{Cl}_{2}\) goes to completion, which of the following would you expect to observe after mixing the two solutions? Explain your answer. (a) The solution formed in experiment 1 will be a darker red. (b) The solution formed in experiment 2 will be a darker red. (c) The solutions formed in both experiments will be the same shade of red.

Carbon disulfide burns in oxygen to form carbon dioxide and sulfur dioxide. $$ \mathrm{CS}_{2}(l)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{SO}_{2}(g) $$ Calculate the number of \(\mathrm{O}_{2}\) molecules it would take to consume 500 molecules of \(\mathrm{CS}_{2}\). Calculate the number of moles of \(\mathrm{O}_{2}\) it would take to consume 5.00 moles of \(\mathrm{CS}_{2}\)

Cocaine is a naturally occurring substance that can be extracted from the leaves of the coca plant, which grows in South America (and is not to be confused with chocolate, or cocoa, which is extracted from the seeds of another South American plant). If the chemical formula for cocaine is \(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{O}_{4} \mathrm{~N},\) what is the percentage by mass of carbon, hydrogen, oxygen, and nitrogen in the compound? Comment on the ease with which elemental analysis of the carbon and hydrogen in a compound can be used to distinguish between the white, crystalline powder known as aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right),\) which is used to cure headaches, and the white, crystalline powder known as cocaine, which is more likely to cause headaches.

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