Problem 29 - Chemistry: Principles and Reactions

Question

Calculate the mass in grams of \(2.688 \mathrm{~mol}\) of (a) chlorophyll, \(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{~N}_{4} \mathrm{O}_{5} \mathrm{Mg}\), responsible for the green color of leaves. (b) sorbitol, \(\mathrm{C}_{9} \mathrm{H}_{14} \mathrm{O}_{6}\), an artificial sweetener. (c) indigo, \(\mathrm{C}_{16} \mathrm{H}_{10} \mathrm{~N}_{2} \mathrm{O}_{2}\), a blue dye.

Step-by-Step Solution

Answer

Question: Calculate the mass in grams for the given compounds with the molar quantities provided. Molar quantities: Chlorophyll: 2.688 mol Sorbitol: 2.688 mol Indigo: 2.688 mol Answer: (a) Chlorophyll: 2403.15 g (b) Sorbitol: 489.38 g (c) Indigo: 705.17 g

Step 1: Identify the molecular formula of chlorophyll

The molecular formula for chlorophyll is \(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{~N}_{4} \mathrm{O}_{5} \mathrm{Mg}\).

Step 2: Calculate the molar mass of chlorophyll

Using the periodic table, we can find the molar masses of the elements in chlorophyll: Carbon (C): 12.01 g/mol Hydrogen (H): 1.008 g/mol Magnesium (Mg): 24.30 g/mol Nitrogen (N): 14.01 g/mol Oxygen (O): 16.00 g/mol So, the molar mass of chlorophyll is: $$(55×12.01) + (72×1.008) + (4×14.01) +(5×16.00) + 24.30 = 893.51 \mathrm{~g/mol}$$

Step 3: Calculate the mass in grams of chlorophyll

Given that we have 2.688 mol of chlorophyll, we can calculate the mass in grams using the molar mass: $$2.688 \mathrm{~mol} × 893.51 \frac{\mathrm{g}}{\mathrm{mol}} = 2403.15 \mathrm{~g}$$ For sorbitol:

Step 1: Identify the molecular formula of sorbitol

The molecular formula for sorbitol is \(\mathrm{C}_{9} \mathrm{H}_{14} \mathrm{O}_{6}\).

Step 2: Calculate the molar mass of sorbitol

Using the molar masses of the elements in sorbitol, we can calculate the molar mass: $$(9×12.01) + (14×1.008) + (6×16.00) = 182.17 \mathrm{~g/mol}$$

Step 3: Calculate the mass in grams of sorbitol

Given that we have 2.688 mol of sorbitol, we can calculate the mass in grams using the molar mass: $$2.688 \mathrm{~mol} × 182.17 \frac{\mathrm{g}}{\mathrm{mol}} = 489.38 \mathrm{~g}$$ For indigo:

Step 1: Identify the molecular formula of indigo

The molecular formula for indigo is \(\mathrm{C}_{16} \mathrm{H}_{10} \mathrm{~N}_{2} \mathrm{O}_{2}\).

Step 2: Calculate the molar mass of indigo

Using the molar masses of the elements in indigo, we can calculate the molar mass: $$(16×12.01) + (10×1.008) + (2×14.01) +(2×16.00) = 262.30 \mathrm{~g/mol}$$

Step 3: Calculate the mass in grams of indigo

Given that we have 2.688 mol of indigo, we can calculate the mass in grams using the molar mass: $$2.688 \mathrm{~mol} × 262.30 \frac{\mathrm{g}}{\mathrm{mol}} = 705.17 \mathrm{~g}$$ Thus, the mass in grams for each compound is: (a) Chlorophyll: 2403.15 g (b) Sorbitol: 489.38 g (c) Indigo: 705.17 g

Key Concepts

Understanding Chlorophyll Molar Mass Calculation

Chlorophyll is an essential pigment in plants, giving them their iconic green hue. Its molecular formula is represented as \(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{N}_{4} \mathrm{O}_{5} \mathrm{Mg}\). To find its molar mass, we use the atomic masses of the individual elements involved, a process which is foundational in chemistry.

• Carbon \((C): 12.01\, \mathrm{g/mol}\)
• Hydrogen \((H): 1.008 \, \mathrm{g/mol}\)
• Nitrogen \((N): 14.01 \, \mathrm{g/mol}\)
• Oxygen \((O): 16.00 \, \mathrm{g/mol}\)
• Magnesium \((Mg): 24.30 \, \mathrm{g/mol}\)

To calculate the molar mass of chlorophyll, we multiply the atomic mass of each element by the number of atoms present, then sum it all up:\[(55 \times 12.01) + (72 \times 1.008) + (4 \times 14.01) + (5 \times 16.00) + 24.30 = 893.51 \, \mathrm{g/mol}\]This molar mass is useful when calculating how much the substance weighs in grams per mole. With 2.688 mol of chlorophyll, the weight calculates to:\[2.688 \, \mathrm{mol} \times 893.51 \, \frac{\mathrm{g}}{\mathrm{mol}} = 2403.15 \, \mathrm{g}\]

Sorbitol and Its Molar Mass

Sorbitol is a sugar alcohol used as an artificial sweetener. Its molecular formula, \(\mathrm{C}_{9} \mathrm{H}_{14} \mathrm{O}_{6}\), helps us calculate its molar mass by summing up the atomic masses.

• Carbon \((C): 12.01 \, \mathrm{g/mol}\)
• Hydrogen \((H): 1.008 \, \mathrm{g/mol}\)
• Oxygen \((O): 16.00 \, \mathrm{g/mol}\)

Calculate by multiplying the atomic masses with the number of atoms:\[(9 \times 12.01) + (14 \times 1.008) + (6 \times 16.00) = 182.17 \, \mathrm{g/mol}\]This lets us find the mass when given moles. For 2.688 mol of sorbitol, compute:\[2.688 \, \mathrm{mol} \times 182.17 \, \frac{\mathrm{g}}{\mathrm{mol}} = 489.38 \, \mathrm{g}\]Understanding these calculations allows us to appreciate how weight relates to amount, crucial for scientific measurements.

Exploring Indigo Dye Molar Mass

Indigo, a significant blue dye, has a molecular formula of \(\mathrm{C}_{16} \mathrm{H}_{10} \mathrm{N}_{2} \mathrm{O}_{2}\). Knowing the molar mass of each element allows the aggregate molar mass calculation for the compound.

• Carbon \((C): 12.01 \, \mathrm{g/mol}\)
• Hydrogen \((H): 1.008 \, \mathrm{g/mol}\)
• Nitrogen \((N): 14.01 \, \mathrm{g/mol}\)
• Oxygen \((O): 16.00 \, \mathrm{g/mol}\)

Perform the calculation by multiplying and adding up the results:\[(16 \times 12.01) + (10 \times 1.008) + (2 \times 14.01) + (2 \times 16.00) = 262.30 \, \mathrm{g/mol}\]For 2.688 mol of indigo dye, the mass is:\[2.688 \, \mathrm{mol} \times 262.30 \, \frac{\mathrm{g}}{\mathrm{mol}} = 705.17 \, \mathrm{g}\]This knowledge illustrates the uniformity of chemistry principles across various compounds, providing a consistent foundation.