Question

A student titrates an unknown amount of potassium hydrogen phthalate \(\left(\mathrm{KHC}_{8} \mathrm{H}_{4} \mathrm{O}_{4}, \text { often abbreviated } \mathrm{KHP}\right)\) with 20.46 \(\mathrm{mL}\) of a 0.1000-M NaOH solution. KHP (molar mass 5 204.22 g/ mol) has one acidic hydrogen. What mass of KHP was titrated (reacted completely) by the sodium hydroxide solution?

Short answer

The mass of KHP that reacted completely with the sodium hydroxide solution is \(0.418 \: \text{g}\).

Step-by-step solution

Calculate the moles of NaOH

Using the volume and concentration of NaOH solution, we will calculate the moles of sodium hydroxide: moles of NaOH = volume (L) x concentration (mol/L) First, we need to convert the volume from mL to L: Volume (L) = 20.46 mL × (1 L / 1000 mL) = 0.02046 L Now, we plug the values: moles of NaOH = (0.02046 L)(0.1000 mol/L) = 0.002046 mol

Calculate the moles of KHP

The balanced chemical equation for the titration reaction between KHP and NaOH is: KHP + NaOH → NaKP + H₂O From this equation, we can see that the reaction is in a 1:1 ratio, meaning 1 mole of KHP reacts with 1 mole of NaOH. Therefore, the moles of KHP that reacted are equal to the moles of NaOH: moles of KHP = moles of NaOH = 0.002046 mol

Calculate the mass of KHP that reacted

Now that we have the moles of KHP, we will convert it to mass using the molar mass of KHP (204.22 g/mol): mass of KHP = moles of KHP × molar mass mass of KHP = (0.002046 mol)(204.22 g/mol) = 0.418 g So, the mass of KHP that reacted completely with the sodium hydroxide solution is 0.418 g.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. In simple terms, it is like a recipe for a meal that tells you how much of each ingredient you need.When dealing with chemical reactions, we use stoichiometry to ensure that we have the right proportions of each chemical involved. For the titration of potassium hydrogen phthalate (KHP) with sodium hydroxide (NaOH), stoichiometry helps us understand how these substances will interact based on their balanced chemical equation.

• The balanced equation for our reaction is: \[\text{KHP} + \text{NaOH} \rightarrow \text{NaKP} + \text{H}_2\text{O}\]
• From this equation, we see a 1:1 molar ratio between KHP and NaOH.
• This means for every mole of KHP used, one mole of NaOH is needed for complete reaction.

Employing stoichiometry allows us to accurately determine the mass of KHP that reacts when a certain amount of NaOH is used, as seen in our problem.

Molar Mass

Molar mass is an essential concept in chemistry and represents the mass of one mole of a given substance. It is measured in grams per mole (g/mol) and acts as a bridge between the amount of substance and its mass.For our titration problem, the molar mass of KHP (potassium hydrogen phthalate) is crucial for converting moles to mass. The molar mass of KHP is given as 204.22 g/mol.

• To find the mass of KHP that reacted, we use the formula:\[\text{Mass} = \text{Moles} \times \text{Molar Mass}\]
• Using the moles calculated (0.002046 mol), the mass can be determined as:\[(0.002046 \text{ mol}) \times (204.22 \text{ g/mol}) = 0.418 \text{ g}\]

Understanding molar mass lets us convert between the moles of a chemical species and its mass, providing a practical application for stoichiometry in hands-on scenarios like titration.

Chemical Equations

Chemical equations are symbolic representations that show the reactants and products in a chemical reaction. They are balanced to respect the law of conservation of mass, meaning the number of each type of atom is the same on both sides of the equation.For the KHP and NaOH reaction, the chemical equation is:\[\text{KHC}_8\text{H}_4\text{O}_4 + \text{NaOH} \rightarrow \text{NaKP} + \text{H}_2\text{O}\]

• This equation represents a 1:1 stoichiometric relationship between the reactants.
• Balancing the equation is crucial to accurately predicting how much of each substance will react or be produced.

In this process, chemical equations provide a roadmap for chemists, helping them calculate reactant requirements or product yields. Knowing how to read and balance these equations is a key skill in chemistry.

Equivalence Point

The equivalence point is a critical concept in titration, representing the moment when the quantity of titrant added is just enough to completely react with the analyte. In an acid-base titration involving KHP and NaOH, reaching the equivalence point means the moles of NaOH added are equal to the moles of KHP present in the solution.

• For our example, because KHP and NaOH react in a 1:1 ratio, the equivalence point occurs when their moles are equal.
• This information allows us to determine the moles and, subsequently, the mass of KHP from the volume and concentration of NaOH used.

Recognizing and accurately determining the equivalence point is vital for calculating concentrations and quantities in various titration experiments, ensuring that the reaction is complete without excess reactants.