Question

How many milligrams \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) must be present in \(50.0 \mathrm{L}\) of a solution containing \(2.35 \mathrm{ppm} \mathrm{Ca} ?\) [Hint: See also Exercise 103 .]

Short answer

Therefore, the mass of \(Ca(NO_3)_2\) present in the solution is approximately 480.25 milligrams.

Step-by-step solution

Convert ppm into milligrams

To convert the concentration from ppm to milligrams, we need to understand that 1 ppm is equivalent to 1 milligram per liter (\(mg/L\)). Therefore, the concentration of Calcium in the solution is 2.35 \(mg/L\).

Calculate the total weight of Calcium

Multiply the volume of the solution by the concentration to find the total weight of Calcium. This is done because the concentration is the amount of a substance per unit volume. So, the total weight of Calcium is equal to 2.35 \(mg/L\) * 50.0 \(L\) = \(117.5 mg\).

Calculate the mass of Calcium Nitrate

To calculate the mass of \(Ca(NO_3)_2\), it is necessary to understand that the weight of Calcium is part of the total weight of \(Ca(NO_3)_2\). So, we need to find the molar mass of Calcium and \(Ca(NO_3)_2\). The atomic masses are approximately: Calcium = 40, Nitrogen = 14, Oxygen = 16. Therefore, the molar mass of \(Ca(NO_3)_2\) is approximately \(40 + 2*(14 + 3*16) = 164 g/mol\). Given that we are dealing with milligrams in this question, it is more convenient to express the molar mass in \(mg\), therefore, the molar mass is \(164,000 mg/mol\). To find the mass of \(Ca(NO_3)_2\) that relates to 117.5 \(mg\) of Calcium, we use the formula: \((117.5 mg \, Ca \times 164,000 mg \, Ca(NO_3)_2)/(40,000 mg \, Ca) = 480.25 mg \, Ca(NO_3)_2\).

Key concepts

Understanding Parts per Million (ppm)

"Parts per million" (ppm) is a unit used to describe the concentration of a substance in a solution. It is particularly useful in quantifying very dilute concentrations. The term "ppm" indicates how many parts of a chemical are present in one million parts of the given solution. In simpler terms, 1 ppm is equivalent to 1 milligram of a substance per liter ( mg/L ) of solution. This makes ppm a handy metric for environmental science, chemistry, and biology, especially when measuring pollutants or contaminants, which are often present in low amounts.

In the context of our problem, we convert 2.35 ppm of calcium into milligrams by multiplying the concentration ( ppm ) by the volume of the solution in liters. This gives us the total amount of calcium present in the solution in milligrams. Remember, the ppm measurement assumes a default density of water, implying 1 liter of water weighs 1 kilogram (or 1,000 grams), a crucial point when dealing with solutions close to this density.

Steps in Molar Mass Calculation

Molar mass is the mass of a given substance (chemical element or chemical compound) divided by its amount of substance. The unit for molar mass is grams per mole ( g/mol ), a crucial unit in stoichiometry for converting between the mass of a substance and the amount of molecules or atoms it contains.

To calculate the molar mass of a compound:

• Identify the elements present in the compound and their respective quantities from the formula.
• Look up the atomic masses of each element from the periodic table.
• Multiply the atomic mass of each element by the number of atoms of that element within the compound.
• Sum the total masses to get the molar mass.

For example, in the calcium nitrate compound ( Ca(NO_3)_2 ), we calculate the molar mass by finding the sum of the atomic masses involved: Calcium (40), Nitrogen (14 * 2), and Oxygen (16 * 6). This computation gives us a molar mass of approximately 164 g/mol. Understanding these steps ensures precision in converting between moles and mass, a vital part in any chemical stoichiometry problem.

The Role and Formula of Calcium Nitrate

Calcium nitrate, symbolized as Ca(NO_3)_2 , is a compound that consists of calcium, nitrogen, and oxygen atoms. It's important in various industrial processes and is used as a fertilizer due to its high solubility and absorptive properties.

In stoichiometry, working with compounds like calcium nitrate requires knowing its molar mass to perform calculations involving chemical reactions or solution concentrations. From our calculations, the molar mass of calcium nitrate is around 164,000 mg/mol, which is crucial when converting between the amount of elemental calcium and the compound Ca(NO_3)_2 .

In our particular problem, after determining the quantity of calcium in milligrams, we find how much of this compound equals that amount of calcium. This involves converting milligrams of calcium to its equivalent in Ca(NO_3)_2 using the respective molar mass, allowing us to calculate the required mass of calcium nitrate in the solution effectively. Understanding and computing this relationship accurately is vital in laboratory settings and ensures precise chemical preparation.