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Chapter 3: Problem 70

When baking soda (sodium bicarbonate or sodium hydrogen carbonate, \(\mathrm{NaHCO}_{3}\) ) is heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, donuts, and bread. (a) Write a balanced equation for the decomposition of the compound (one of the products is \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) ). (b) Calculate the mass of \(\mathrm{NaHCO}_{3}\) required to produce \(20.5 \mathrm{~g}\) of \(\mathrm{CO}_{2}\)

Short Answer

Expert verified
\(\mathrm{NaHCO}_{3}\) decomposes to produce \(\mathrm{Na}_{2} \mathrm{CO}_{3} + H_{2}O + CO_{2}\) and approximately 39.02g of \(\mathrm{NaHCO}_{3}\) is required to produce 20.5 g of \(CO_{2}\)

Step by step solution

01

Write the Unbalanced Equation

First, an unbalanced equation should be written to denote the decomposition of Sodium Bicarbonate \(\mathrm{NaHCO}_{3}\). Considering that one product is Sodium Carbonate \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) and knowing that decomposing bicarbonate usually also produces Water \(H_{2}O\) and Carbon Dioxide \(CO_{2}\), the unbalanced chemical equation should look as follows: \(\mathrm{NaHCO}_{3} \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3} + H_{2}O + CO_{2}\)
02

Balance the Equation

Secondly, balance the equation to ensure the law of conservation of mass is obeyed. This is done by adjusting coefficients in front of formulas as required. The balanced equation is: \(2\mathrm{NaHCO}_{3} \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3} + H_{2}O + CO_{2}\)
03

Calculate Molar Masses

Before performing stoichiometric calculations, determine the molar masses of sodium bicarbonate \(\mathrm{NaHCO}_{3}\) and carbon dioxide \(\mathrm{CO}_{2}\). It should result in approximately 84.007 g/mol for \(\mathrm{NaHCO}_{3}\) and 44.01 g/mol for \(\mathrm{CO}_{2}\).
04

Use Stoichiometry to Solve for Mass

In this step, use stoichiometric relationships and the molar masses calculated in the previous step to find out the mass of \(\mathrm{NaHCO}_{3}\) needed to produce 20.5 g of \(\mathrm{CO}_{2}\). This is done by first converting the mass of \(\mathrm{CO}_{2}\) to moles using its molar mass, then using the stoichiometric ratio from the balanced chemical equation to figure out the number of moles of \(\mathrm{NaHCO}_{3}\) required. Lastly, convert this moles of \(\mathrm{NaHCO}_{3}\) to grams using its molar mass. It will give the appropriate solution.

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Most popular questions from this chapter

Why is the theoretical yield of a reaction determined only by the amount of the limiting reactant?

A sample of iron weighing \(15.0 \mathrm{~g}\) was heated with potassium chlorate \(\left(\mathrm{KClO}_{3}\right)\) in an evacuated container. The oxygen generated from the decomposition of \(\mathrm{KClO}_{3}\) converted some of the Fe to \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). If the combined mass of Fe and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) was \(17.9 \mathrm{~g}\), calculate the mass of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) formed and the mass of \(\mathrm{KClO}_{3}\) decomposed.

Without doing any detailed calculations, arrange the following substances in the increasing order of number of moles: \(20.0 \mathrm{~g} \mathrm{Cl}, 35.0 \mathrm{~g} \mathrm{Br},\) and\(94.0 \mathrm{~g} \mathrm{I}\)

An iron bar weighed \(664 \mathrm{~g}\). After the bar had been standing in moist air for a month, exactly one-eighth of the iron turned to rust \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right) .\) Calculate the final mass of the iron bar and rust.

Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is the gas that is mainly responsible for global warming (the greenhouse effect). The burning of fossil fuels is a major cause of the increased concentration of \(\mathrm{CO}_{2}\) in the atmosphere. Carbon dioxide is also the end product of metabolism (see Example 3.13 ). Using glucose as an example of food, calculate the annual human production of \(\mathrm{CO}_{2}\) in grams, assuming that each person consumes \(5.0 \times 10^{2} \mathrm{~g}\) of glucose per day. The world's population is 7.2 billion, and there are 365 days in a year.
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