Question

A sodium dihydrogen phosphate solution was prepared by dissolving \(5.0 \mathrm{g}\) of \(\mathrm{NaH}_{2} \mathrm{PO}_{4}\) in enough water to make \(500 .\) mL of solution. What are the molarity and normality of the resulting solution?

Short answer

The molarity of the sodium dihydrogen phosphate (\(NaH_{2}PO_{4}\)) solution is 0.0834 M, calculated by dividing the number of moles of \(NaH_{2}PO_{4}\), which is 0.0417 mol, by the volume of the solution in liters (0.500 L). The normality of the solution is 0.0834 N, determined by dividing the number of equivalents (0.0417 mol x 1 equivalent/mol) by the volume of the solution in liters (0.500 L).

Step-by-step solution

Calculate the number of moles of NaH2PO4

To calculate the number of moles of NaH2PO4, we will need to find the molar mass of the compound. The molar mass is found by adding up the atomic masses of each element in the compound. Na = 22.99 g/mol, H = 1.01 g/mol, P = 30.97 g/mol, O = 16.00 g/mol Molar mass of NaH2PO4 = (1 x 22.99) + (2 x 1.01) + (1 x 30.97) + (4 x 16.00) = 119.98 g/mol Now, we can find the number of moles using the mass of NaH2PO4 and its molar mass: Number of moles = mass / molar mass = 5.0 g / 119.98 g/mol = 0.0417 mol

Calculate the volume of the solution in liters

Since the volume of the solution is given in milliliters, we need to convert it to liters. Volume in liters = 500 mL ÷ 1000 = 0.500 L

Calculate the molarity of the solution

With the number of moles and volume determined, we can now calculate the molarity of the solution. Molarity = moles / volume = 0.0417 mol / 0.500 L = 0.0834 M

Determine the number of equivalents per mole of NaH2PO4

To determine the number of equivalents per mole of NaH2PO4, we need to identify how many H+ ions can be donated by one molecule of the compound. In NaH2PO4, there is one dissociable H+ ion. Therefore, each mole of NaH2PO4 can donate one equivalent of H+ ions.

Calculate the normality of the solution

Now that we know the number of equivalents per mole of NaH2PO4, we can calculate the normality of the solution. Normality = equivalents / volume = (0.0417 mol x 1 equivalent/mol) / 0.500 L = 0.0834 N The molarity of the resulting NaH2PO4 solution is 0.0834 M, and the normality of the solution is 0.0834 N.

Key concepts

Understanding Normality

Normality is a concept that helps us understand the concentration of solutions based on the reactive capacity of a solute. While molarity (M) refers to the number of moles of solute per liter of solution, normality (N) goes a step further to consider the number of equivalents of the reactive species contained in the solution.

Here's how we can break it down:

• Normality is often used in acid-base reactions, redox reactions, and precipitation reactions.
• In the context of sodium dihydrogen phosphate (\(\text{NaH}_{2}\text{PO}_{4}\)), the reactive species is the H⁺ ion that the compound can donate.
• Each mole of \(\text{NaH}_{2}\text{PO}_{4}\) can donate one H⁺ ion, thus each mole is equivalent to one equivalent.

Therefore, the normality of a solution containing 0.0417 moles of \(\text{NaH}_{2}\text{PO}_{4}\) in 0.500 liters of water is equivalent to its molarity, hence 0.0834 N.

Understanding Molar Mass

The molar mass of a compound is the mass of one mole of that compound expressed in grams per mole (g/mol). It helps us convert between grams of a substance and the number of moles, which makes it a crucial concept in chemistry.

Here's how to compute the molar mass for sodium dihydrogen phosphate (\(\text{NaH}_{2}\text{PO}_{4}\)):

• Identify the atomic masses of each constituent element: Sodium (Na) = 22.99 g/mol, Hydrogen (H) = 1.01 g/mol, Phosphorus (P) = 30.97 g/mol, and Oxygen (O) = 16.00 g/mol.
• Add together the atomic masses while considering the number of each type of atom in the formula:\(1 \times 22.99\) + \(2 \times 1.01\) + \(1 \times 30.97\) + \(4 \times 16.00\).
• The total adds up to 119.98 g/mol for \(\text{NaH}_{2}\text{PO}_{4}\).

This calculated molar mass can then be used to determine the number of moles in a given mass of the compound.

Sodium Dihydrogen Phosphate: A Key Compound

Sodium dihydrogen phosphate, with the chemical formula \(\text{NaH}_{2}\text{PO}_{4}\), plays an important role in various chemical applications due to its properties as a salt of phosphoric acid.

Here are some of its key features:

• It exists as a white crystalline powder which is highly soluble in water, making it ideal for preparing solutions.
• In a solution, it acts as a source of phosphoric acids and is often used as a buffer to maintain pH stability.
• It's commonly used in cleaning agents, food preservatives, and as a laxative in medicine.

Understanding sodium dihydrogen phosphate's role in chemical reactions helps us comprehend the significance of its normality in solution, as it actively contributes to the chemistry via its ability to donate hydrogen ions.