Problem 54 - Chemistry: Principles and Reactions

Question

A child eats \(10.0 \mathrm{~g}\) of paint containing \(5.0 \% \mathrm{~Pb}\). How many grams of the sodium salt of EDTA, \(\mathrm{Na}_{4}(\mathrm{EDTA})\), should he receive to bring the lead into solution as \(\mathrm{Pb}\). EDTA?

Step-by-Step Solution

Answer

Answer: To determine the grams of Na4(EDTA) needed, follow these steps: 1. Calculate the mass of lead (Pb) ingested by the child. 2. Determine the moles of lead (Pb) ingested. 3. Determine the moles of Na4(EDTA) required based on the stoichiometry of the reaction. 4. Calculate the mass of Na4(EDTA) required.

Step 1: Calculate the mass of lead (Pb) ingested

First, calculate the mass of lead that the child ingested. The child ingested 10.0 grams of paint, which has a 5.0% lead content. To find the mass of the lead, multiply the total mass by the percentage of lead: Mass of lead (Pb) = (10.0 g paint) × (0.050) Calculate the mass of lead (Pb).

Step 2: Determine the moles of lead (Pb) ingested

Next, find the moles of lead the child ingested using the molar mass of lead (Pb). Molar mass of lead is approximately 207.2 g/mol. Moles of lead = (mass of lead) / (molar mass of lead) Calculate the moles of lead (Pb).

Step 3: Determine the moles of Na4(EDTA) required

In this step, use stoichiometry to find out moles of Na4(EDTA) required to bring the same amount of lead into the solution as Pb.EDTA. The reaction between lead and EDTA is a 1:1 reaction, meaning that for each mole of lead (Pb), one mole of Na4(EDTA) is needed. Moles of Na4(EDTA) = Moles of lead (Pb)

Step 4: Calculate the mass of Na4(EDTA) required

Finally, find the mass of Na4(EDTA) required by multiplying the moles of Na4(EDTA) by its molar mass. The molar mass of Na4(EDTA) is approximately 380.2 g/mol. Mass of Na4(EDTA) = (moles of Na4(EDTA)) × (molar mass of Na4(EDTA)) Calculate the mass of Na4(EDTA). The result will show how many grams of Na4(EDTA) the child should receive to bring the ingested lead into solution as Pb.EDTA.

Key Concepts

Lead Poisoning

Lead poisoning occurs when lead—a harmful heavy metal—accumulates in the body, often through ingestion or inhalation. Children are particularly vulnerable due to their smaller body size and developing systems, and it can cause a range of health problems. Lead affects the nervous system, kidneys, and can impair cognitive functions. It's often found in older paints, which is why precautions must be taken in environments with potential lead exposure. If a child ingests or inhales lead, it's critical to reduce and remove it from the body promptly to prevent serious health consequences.
Symptoms of lead poisoning can include:

• Developmental delay
• Irritability
• Weight loss
• Fatigue
• Abdominal pain
• Hearing loss

Early interventions and treatments can help mitigate these effects and are necessary for reversing some symptoms of lead exposure.

Chelation Therapy

Chelation therapy is a medical procedure used to remove heavy metals like lead from the bloodstream. It involves the administration of chelating agents, which bind to the metals and facilitate their excretion from the body. In the case of lead poisoning, a common agent used is EDTA (Ethylenediaminetetraacetic acid), a molecule known for its ability to bind metal ions tightly. EDTA can be combined with lead to form a complex that is easily excreted usually through urine, helping to lower the concentration of lead in the bloodstream quickly.
Chelation therapy is:

• Critical for severe cases of lead poisoning
• Administered under medical supervision
• Effective but needs careful monitoring for side effects like kidney damage

The process, typically part of a comprehensive treatment plan, may include dietary changes and addressing the source of lead exposure.

Molar Mass Calculation

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance. Calculating molar mass involves summing up the atomic masses of all the elements in a compound. This is important in stoichiometry, where it allows for conversions between grams and moles in chemical reactions. For instance, in the exercise, the molar mass of lead (Pb) is used to convert the mass of ingested lead from grams to moles, using the approximate molar mass of 207.2 g/mol.
Steps to calculate molar mass include:

• Identify the elements in the compound
• Find the atomic mass of each element (usually found on the periodic table)
• Multiply the atomic mass by the number of atoms of that element in the compound
• Sum all the values to get the molar mass of the compound

For \(\mathrm{Na}_{4}(\mathrm{EDTA})\), these calculations help in determining how much is required to treat the lead ingestion effectively.

Chemical Reaction Balance

Chemical reaction balance is essential in stoichiometry and involves ensuring that the number of atoms for each element is the same on both sides of a chemical equation. This reflects the conservation of mass, a core principle in chemistry stating that matter cannot be created or destroyed.
Balancing equations is crucial for:

• Ensuring correct stoichiometric calculations
• Understanding the relationship between reactants and products
• Predicting the amounts of products generated

In the context of chelation therapy involving EDTA and lead, the balance is seen in the 1:1 molar ratio between EDTA and lead in forming lead-EDTA complex. This balance guides us in determining how much EDTA is required for effective treatment, ensuring that for each mole of lead present, one mole of EDTA is used to form the complex, facilitating its excretion from the body.