Problem 74 - General Chemistry: Principles and Modern Applications

Question

A \(110.520 \mathrm{g}\) sample of mineral water is analyzed for its magnesium content. The \(\mathrm{Mg}^{2+}\) in the sample is first precipitated as \(\mathrm{MgNH}_{4} \mathrm{PO}_{4},\) and this precipitate is then converted to \(\mathrm{Mg}_{2} \mathrm{P}_{2} \mathrm{O}_{7},\) which is found to weigh 0.0549 g. Express the quantity of magnesium in the sample in parts per million (that is, in grams of \(\mathrm{Mg}\) per million grams of \(\mathrm{H}_{2} \mathrm{O}\) ).

Step-by-Step Solution

Answer

Using the steps described, calculate the ppm of magnesium using the given amounts. After completion, the exact quantity of magnesium in parts per million in the sample will be obtained.

Step 1: Calculate the Molar Mass of Compounds

To make the necessary conversions from grams to moles, it's key to know the molar mass of the compounds. Here's how to calculate these values:\n The molar mass of \(Mg_{2} P_{2} O_{7}\) is \(2 * 24.305 (Mg) + 2 * 30.974 (P) + 7 * 16.00 (O) = 222.57 g/mol\), and \nThe molar mass of Mg is \(24.305 g/mol\).

Step 2: Convert \(Mg_{2} P_{2} O_{7}\) to Mg

Since you know the weight of \(Mg_{2} P_{2} O_{7}\) to be 0.0549 g and it contains Magnesium which you need to find the concentration off. Use the molar mass to convert from grams of \(Mg_{2} P_{2} O_{7}\) to grams of Mg.\n \(\frac{(0.0549 g * 1 mol) / 222.57 g/mol * (2 mol Mg)\}{1 mol Mg_{2} P_{2} O_{7}} * 24.305 g/mol Mg\). The molar quantities cancel out leaving the quantity of Mg in the \(Mg_{2} P_{2} O_{7}\) in grams.

Step 3: Calculate the ppm of Mg

Use the mass of the water sample and the mass of magnesium calculated in the previous step to obtain the quantity of Mg in parts per million. Parts per million is defined as the mass of the substance divided by total mass times 1,000,000. The calculation to find ppm of Magnesium is then \(\frac{Mg (g)}{total mass (g)} * 1,000,000\)

Key Concepts

Molar Mass Calculation

Calculating the molar mass of a compound is an essential step in many chemical equations. It's the sum of the atomic masses of all atoms in a molecule. Knowing the molar mass allows us to convert between grams and moles, which is critical for reacting quantities.

In this example, we need the molar mass of magnesium pyrophosphate (\(\mathrm{Mg}_{2} \mathrm{P}_{2} \mathrm{O}_{7}\)). By adding up the atomic weights as follows:

• Magnesium (\(\mathrm{Mg}\)): 24.305 g/mol, and there are two magnesium atoms.
• Phosphorus (\(\mathrm{P}\)): 30.974 g/mol, and there are two phosphorus atoms.
• Oxygen (\(\mathrm{O}\)): 16.00 g/mol, with seven oxygen atoms.

The total molar mass will be computed as \(2 \times 24.305 + 2 \times 30.974 + 7 \times 16.00 = 222.57 \mathrm{g/mol}\).

This value is pivotal, as it allows us to determine the amount of magnesium present within the compound.

Precipitation Reaction

A precipitation reaction is a process where cations and anions in aqueous solution combine to form an insoluble compound, or precipitate.

In our scenario, the \(\mathrm{Mg}^{2+}\) ions from the mineral water combine with\(\mathrm{NH}_{4} \mathrm{PO}_{4}\) ions to form magnesium ammonium phosphate (\(\mathrm{MgNH}_{4} \mathrm{PO}_{4}\)), a solid precipitate. This step is important, as it isolates the magnesium from the rest of the solution, making it easier to process.

The solid \(\mathrm{MgNH}_{4} \mathrm{PO}_{4}\) is then transformed into \(\mathrm{Mg}_{2} \mathrm{P}_{2} \mathrm{O}_{7}\) for accurate measurement. These transformations ensure that we focus specifically on magnesium by converting it into a form with known proportions.

Parts Per Million (ppm)

Parts per Million (ppm) is a way to express very dilute concentrations of substances. It is especially useful in contexts like environmental studies or chemistry, where trace amounts need accurate measurement.

To calculate ppm for magnesium in this problem, the mass of magnesium obtained through conversion is divided by the total mass of the sample, then multiplied by 1,000,000:
\[\text{ppm} = \left(\frac{\text{mass of Mg (g)}}{\text{total mass of water sample (g)}}\right) \times 1,000,000\]This expresses the concentration of magnesium per million grams of the sample, providing a clear metric for comparing different concentrations.

Using ppm allows scientists and engineers to communicate findings about trace materials effectively, aiding understanding and regulation in various fields.