Problem 110 - Chemistry: The Central Science

Question

Lead glass contains \(18-40 \%\) by mass of \(\mathrm{PbO}\) (instead of \(\mathrm{CaO}\) in regular glass). Lead glass is still used industrially, but "lead crystal" drinking goblets are no longer considered safe, as the lead may leach out and cause toxic responses in humans. A particular 286-g lead crystal goblet that holds \(450 \mathrm{~mL}\) of liquid is \(27 \%\) PbO by mass, and it leaches \(3.4\) micrograms of lead every time it is filled. How many grams of sodium sulfide would be required to decontaminate all the lead in the entire goblet?

Step-by-Step Solution

Answer

To decontaminate all the lead in the 286-g lead crystal goblet, 21.67 grams of sodium sulfide would be required.

Step 1: Find the mass of PbO in the goblet

We are given that the goblet has a mass of 286 g, and it is 27% PbO by mass. We can use this information to find the mass of PbO: Mass of PbO = (Total mass of goblet) x (Percentage of PbO by mass) Mass of PbO = 286 g x 0.27 = 77.22 g

Step 2: Find the mass of lead in the PbO

Now that we have the mass of PbO, we need to find the mass of lead in it. For this, we will use the molar mass of Pb and PbO to determine the mass of lead in the 77.22 grams of PbO. Molar mass of Pb = 207.2 g/mol Molar mass of PbO = 207.2 (Pb) + 16 (O) = 223.2 g/mol The ratio of Pb mass to PbO mass is equal to the ratio of their molar masses: (Pb mass)/(PbO mass) = (Pb molar mass)/(PbO molar mass) Let's solve for the mass of lead (Pb mass): Pb mass = (PbO mass) x (Pb molar mass) / (PbO molar mass) Pb mass = 77.22 g * (207.2 g/mol) / (223.2 g/mol) = 71.83 g

Step 3: Calculate the mass of sodium sulfide required

Finally, we need to find the mass of sodium sulfide required to decontaminate the entire amount of lead in the goblet using stoichiometry. To do this, we need to know the balanced chemical equation for the reaction between lead and sodium sulfide: Pb + Na2S → PbS + 2 Na Using the molar masses of lead (Pb), sodium (Na), and sodium sulfide (Na2S), we can calculate the mass of sodium sulfide needed: Molar mass of Na = 23 g/mol Molar mass of Na2S = 2 x 23 (Na) + 32 (S) = 78 g/mol We will now use the stoichiometry method to find the mass of Na2S needed to react with 71.83 grams of lead: Mass of Na2S = (Mass of Pb) x (Molar mass of Na2S) / (Molar mass of Pb) x (Stoichiometry ratio) Mass of Na2S = 71.83 g * (78 g/mol) / (207.2 g/mol) x (1/1) = 21.67 g So, 21.67 grams of sodium sulfide would be required to decontaminate all the lead in the entire goblet.

Key Concepts

Lead Glass

Lead glass is a special type of glass that incorporates lead oxide (PbO) in its composition, which differentiates it from regular glass where calcium oxide (CaO) is usually used. This can make lead glass heavier and give it a higher refractive index, meaning it can sparkle more like a diamond. However, there are downsides. Lead glass can pose health risks if used improperly, like in drinking vessels, because the lead can leach out into liquids. This is why items such as lead crystal goblets are no longer popular for use in households. The industrial use of lead glass remains acceptable for applications where lead exposure is not a risk to health.

In the case of our exercise, we need to address the lead content in a goblet. This goblet is 27% lead oxide by mass, showing just how prevalent lead is in this material.

Molar Mass

Molar mass is an important concept in stoichiometry, especially when dealing with reactions involving compounds like lead oxide (PbO). Molar mass is the mass of one mole of a substance. It's calculated by adding the atomic masses of all atoms in a molecule. For lead oxide, the molar mass involves the sum of the mass of lead (207.2 g/mol) and oxygen (16 g/mol), making PbO's molar mass 223.2 g/mol.

Understanding molar mass helps us convert between mass and moles of a substance. In the exercise given, we used the molar masses of both lead (Pb) and lead oxide (PbO) to find out how much lead is present in our goblet. Such conversions are essential for determining how much of a reactant is needed or how much of a product will be formed in a chemical reaction.

Chemical Reaction

Chemical reactions are processes where reactant substances turn into products. In stoichiometry, we use balanced chemical equations to understand how reactants convert into products. The exercise demonstrates the reaction of lead with sodium sulfide (Na\(_2\)S). The balanced reaction is:

\[ \text{Pb} + \text{Na}_2\text{S} \rightarrow \text{PbS} + 2 \text{Na} \]

This equation helps us determine the stoichiometry, or the quantitative relationships, between reactants and products. The given stoichiometric ratios tell us that one mole of lead reacts with one mole of sodium sulfide to produce lead sulfide (PbS) and sodium (Na).

Using stoichiometry, we calculated the mass of sodium sulfide needed to fully react with all the lead in the goblet, ensuring that no lead remains to pose a toxic threat.

Toxicology

Toxicology is the study of the adverse effects of substances on living organisms. When studying materials like lead glass, understanding toxicology is crucial due to the potential health risks, primarily because lead exposure can result in serious health problems.

Lead is toxic to humans and can cause issues such as nervous system damage, developmental delays in children, and other health disorders. The goblet in the exercise underscores this risk, as it leaches lead when filled with liquid. Drinking from such goblets can lead to lead poisoning over time.

Understanding the lead content and employing chemical reactions, like the one involving sodium sulfide, can help in decontaminating lead, thus reducing potential health risks. This exercise demonstrates the intersection of chemistry and toxicology, where stoichiometric calculations play a role in mitigating toxic exposure.