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Chapter 3: Problem 29

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.

Short Answer

Expert verified
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 by step solution

01

Identify the molecular formula of chlorophyll

The molecular formula for chlorophyll is \(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{~N}_{4} \mathrm{O}_{5} \mathrm{Mg}\).
02

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: $$(55×12.01) + (72×1.008) + (4×14.01) +(5×16.00) + 24.30 = 893.51 \mathrm{~g/mol}$$
03

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:
04

Identify the molecular formula of sorbitol

The molecular formula for sorbitol is \(\mathrm{C}_{9} \mathrm{H}_{14} \mathrm{O}_{6}\).
05

Calculate the molar mass of sorbitol

Using the molar masses of the elements in sorbitol, we can calculate the molar mass: $$(9×12.01) + (14×1.008) + (6×16.00) = 182.17 \mathrm{~g/mol}$$
06

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:
07

Identify the molecular formula of indigo

The molecular formula for indigo is \(\mathrm{C}_{16} \mathrm{H}_{10} \mathrm{~N}_{2} \mathrm{O}_{2}\).
08

Calculate the molar mass of indigo

Using the molar masses of the elements in indigo, we can calculate the molar mass: $$(16×12.01) + (10×1.008) + (2×14.01) +(2×16.00) = 262.30 \mathrm{~g/mol}$$
09

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

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Most popular questions from this chapter

When three moles of a metal oxide, \(\mathrm{MO}_{2}\), react with ammonia gas, the metal (M), water, and nitrogen gas are formed. (a) Write a balanced equation to represent the reaction. (b) When \(13.8 \mathrm{~g}\) of ammonia react with an excess of metal oxide, \(126 \mathrm{~g}\) of \(\mathrm{M}\) are formed. What is the molar mass for \(\mathrm{M}\) ? What is the identity of \(\mathrm{M} ?\)

Some brands of salami contain \(0.090 \%\) sodium benzoate \(\left(\mathrm{NaC}_{7} \mathrm{H}_{5} \mathrm{O}_{2}\right)\) by mass as a preservative. If you eat \(6.00 \mathrm{oz}\) of this salami, how many atoms of sodium will you consume, assuming salami contains no other source of that element?

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