Question

The compound cisplatin, \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2},\) has been studied as an antitumor agent. Cisplatin is synthesized as follows: $$ \mathrm{K}_{2} \mathrm{PtCl}_{4}(a q)+2 \mathrm{NH}_{3}(a q) \rightarrow \operatorname{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}(s)+2 \mathrm{KCl}(a q) $$ What mass of cisplatin can be produced from \(100 .\) g of \(\mathrm{K}_{2} \mathrm{PtCl}_{4}\) and sufficient \(\mathrm{NH}_{3} ?\)

Short answer

The mass of cisplatin that can be produced from 100 grams of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\) and sufficient \(\mathrm{NH}_{3}\) is approximately 79.49 grams.

Step-by-step solution

Calculate the molar mass of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\)

First, we need to find the number of moles in 100g of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\). To do this, we have to find the molar mass of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\). Using periodic table, we can find the atomic mass of each element: Molar mass of K = 39.10 g/mol, Molar mass of Pt = 195.08 g/mol, Molar mass of Cl = 35.45 g/mol. So, the molar mass of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\) is: Molar Mass = (2 × 39.10) + (1 × 195.08) + (4 × 35.45) g/mol = 78.20 + 195.08 + 141.80 g/mol = 415.08 g/mol.

Find the moles of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\)

To find the moles of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\), we can use the formula: Moles = Mass (g) / Molar Mass (g/mol) Moles of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\) = 100g / 415.08 g/mol = 0.2409 mol. Note that the stoichiometry of the given equation implies that one mole of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\) reacts to form one mole of cisplatin, as we can see: \(\mathrm{K}_{2}\mathrm{PtCl}_{4}(a q)+2\mathrm{NH}_{3}(a q)\rightarrow \mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2}\mathrm{Cl}_{2}(s)+2\mathrm{KCl}(a q)\).

Calculate the molar mass of cisplatin

To find the mass of cisplatin produced, we first need to calculate the molar mass of \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\). Using periodic table, we can find the atomic mass of Pt, N, and H: Molar mass of Pt = 195.08 g/mol, Molar mass of N = 14.01 g/mol, Molar mass of H = 1.008 g/mol, Molar mass of Cl = 35.45 g/mol. So, the molar mass of \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\) is: Molar Mass = (1 × 195.08) + (4 × 14.01) + (8 × 1.008) + (2 × 35.45) g/mol= 195.08 + 56.04 + 8.084 + 70.90 g/mol = 330.104 g/mol.

Calculate the mass of cisplatin produced

Now, we can calculate the mass of cisplatin produced by using the moles of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\) and the mole-to-mole relation between it and cisplatin: Moles of cisplatin = 0.2409 mol Now, we can convert the moles of cisplatin to mass: Mass of cisplatin = Moles × Molar Mass = 0.2409 mol × 330.104 g/mol = 79.49 grams. So, the mass of cisplatin that can be produced from 100 grams of \(\mathrm{K}_{2}\mathrm{PtCl}_{4}\) and sufficient \(\mathrm{NH}_{3}\) is approximately 79.49 grams.

Key concepts

Molar Mass Calculation

Understanding molar mass is crucial for solving stoichiometry problems. The molar mass indicates the mass of one mole of a substance. To determine this, you sum the atomic masses of all elements in the compound according to their quantities. For instance, in the compound \( \mathrm{K}_{2}\mathrm{PtCl}_{4} \), you have two potassium (K) atoms, one platinum (Pt) atom, and four chlorine (Cl) atoms. Using atomic masses from the periodic table:

• Potassium (K) = 39.10 g/mol
• Platinum (Pt) = 195.08 g/mol
• Chlorine (Cl) = 35.45 g/mol

Calculate the molar mass by multiplying the atomic mass of each element by its number of atoms and summing up the results:\[\text{Molar Mass of } \mathrm{K}_{2}\mathrm{PtCl}_{4} = (2 \times 39.10) + (1 \times 195.08) + (4 \times 35.45) = 415.08 \text{ g/mol}\]Once the molar mass is known, you can find the number of moles present by dividing the total mass of the compound by its molar mass.

Chemical Reactions

Every chemical reaction involves reactants turning into products. In stoichiometry, chemical equations represent these transformations. The coefficients in a balanced equation tell us the ratio in which substances react. For the synthesis of cisplatin:\[ \mathrm{K}_{2} \mathrm{PtCl}_{4}(aq) + 2 \mathrm{NH}_{3}(aq) \rightarrow \operatorname{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}(s) + 2 \mathrm{KCl}(aq) \]This equation shows that one mole of \( \mathrm{K}_{2} \mathrm{PtCl}_{4} \) reacts with two moles of \( \mathrm{NH}_{3} \) to produce one mole of cisplatin and two moles of \( \mathrm{KCl} \). The stoichiometric coefficients (the numbers before the chemical formulas) help determine how much of each reactant is needed and how much product can be formed. This molecular ratio is essential for calculating the yield of a chemical reaction.

Antitumor Compounds

Antitumor compounds are substances that can prevent or hinder tumor development. They play a critical role in cancer treatment. Cisplatin, \( \operatorname{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2} \), is a well-known antitumor agent used in various chemotherapy regimens. It works by binding to DNA in cancer cells, preventing their replication and leading to cell death. While effective, cisplatin can also have side effects, impacting healthy cells in the body.The development and use of antitumor compounds rely heavily on chemistry, particularly in understanding molecular interactions and side effects. Calculating precisely how much cisplatin can be produced is essential in ensuring an effective and safe dose for treatment.