Problem 67 - Chemistry The Science in Context

Question

Fish Kills High concentrations of ammonia (NH \(_{3}\) ), nitrite ion, and nitrate ion in water can kill fish. Lethal concentrations of these species for rainbow trout are \(1.1 \mathrm{mg} / \mathrm{L}, 0.40 \mathrm{mg} / \mathrm{L},\) and \(1361 \mathrm{mg} / \mathrm{L},\) respectively. Express these concentrations in molality units, assuming a solution density of \(1.00 \mathrm{g} / \mathrm{mL}\)

Step-by-Step Solution

Answer

Answer: The molality values of NH3, NO2-, and NO3- are 6.46 x 10^{-5} mol/kg, 8.69 x 10^{-6} mol/kg, and 0.02195 mol/kg, respectively.

Step 1: Molecular weights

Firstly, we need to find the molecular weights of ammonia (NH3), nitrite ion (NO2-), and nitrate ion (NO3-). The molecular weights are: NH3: N(14.01) + 3H(1.01) = 17.03 g/mol NO2-: N(14.01) + 2O(16.00) = 46.01 g/mol NO3-: N(14.01) + 3O(16.00) = 62.01 g/mol

Step 2: Convert mg/L to g/L

Now, we need to convert the given concentrations to g/L since molecular weights are in g/mol. Divide each concentration by 1000 as 1 mg = 0.001 g. For NH3: 1.1 mg/L = 1.1/1000 = 0.0011 g/L For NO2-: 0.40 mg/L = 0.40/1000 = 0.0004 g/L For NO3-: 1361 mg/L = 1361/1000 = 1.361 g/L

Step 3: Convert g/L to mol/L

To convert g/L to mol/L, we need to divide the g/L values by the corresponding molecular weights. For NH3: (0.0011 g/L) / (17.03 g/mol) = 6.46 x 10^{-5} mol/L For NO2-: (0.0004 g/L) / (46.01 g/mol) = 8.69 x 10^{-6} mol/L For NO3-: (1.361 g/L) / (62.01 g/mol) = 0.02195 mol/L

Step 4: Convert mol/L to molality

Now, we can convert mol/L to molality using the given solution density of 1.00 g/mL. Since the density is 1.00 g/mL and we have 1 L = 1000 mL, the mass of 1 L of the solution is 1000 g. Molality is defined as moles of solute per kilogram of solvent. As we have 1 kg (1000 g) of solvent, the molality is the same as moles of solute (mol/L in this case). So, the molality of each species is: For NH3: 6.46 x 10^{-5} mol/kg For NO2-: 8.69 x 10^{-6} mol/kg For NO3-: 0.02195 mol/kg

Key Concepts

Molality

The concentration of a substance in a solution can be expressed in various ways, but one important unit is molality. Molality, often denoted as 'm', is a measure of the amount of solute in a given mass of solvent. It is defined as the number of moles of solute per kilogram of solvent. Mathematically, molality can be expressed as:
\[ m = \frac{moles\ of\ solute}{kilograms\ of\ solvent} \]
Unlike molarity, which depends on the volume of the solution, molality is based solely on the mass of the solvent, making it independent of temperature and pressure. This characteristic makes molality particularly useful in calculations involving changes in physical conditions, such as boiling point elevation and freezing point depression. In the context of the given exercise, the molality of each substance was calculated by first determining the number of moles from their respective concentrations and then relating that to the mass of water (solvent) in kilograms.

Solution Density

Solution density is a crucial concept in chemistry, serving as the bridge between mass and volume measurements. It is expressed as the mass of the solution per unit volume, commonly in grams per milliliter (g/mL) or kilograms per liter (kg/L). Understanding solution density allows us to convert between different concentration units, such as moving from molarity to molality or vice versa. The density of a solution can affect its physical properties and is often used when preparing laboratory solutions or in industrial applications. In exercises like the given one, assuming a solution density of 1.00 g/mL simplifies calculations since the mass of 1 liter of the solution equates to 1000 g, which is conveniently the mass needed for molality calculations.

Molecular Weight

The molecular weight (or molecular mass) of a substance is the sum of the atomic masses of all atoms in a molecule. It is measured in atomic mass units (amu), with one mole of the substance having a mass in grams equal to the molecular weight. Thus, the molecular weight provides a link between the microscopic world of atoms and molecules and the macroscopic world that we can measure. In chemistry, this concept is foundational for converting between moles and grams, as seen in stoichiometry and concentration calculations. For instance, the molecular weights of ammonia (NH3), nitrite ion (NO2-), and nitrate ion (NO3-) were central to determining the number of moles in the exercise, which later allowed the conversion to molality.

Concentration Conversion

In chemistry, concentration conversion is essential for expressing how much solute is present in a given amount of solution or solvent. Different situations and calculations may require concentration to be expressed as molarity, molality, percent composition, or parts per million, among other units. Mastery of conversion techniques ensures accurate solution preparation and reaction prediction. For example, in the given problem, converting lethal concentrations of ammonia, nitrite ion, and nitrate ion from milligrams per liter (mg/L) to molality required a clear understanding of the relationships between these units. Such conversions often involve multiple steps, including changing mass to moles (using molecular weight) and volume to mass (using solution density), before reaching the desired concentration unit.