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Chapter 16: Problem 84

A typical reaction between an antacid and the hydrochloric acid in gastric juice is \(\mathrm{NaHCO}_{3}(a q)+\mathrm{HCl}(a q) \longrightarrow\) $$\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)$$ Calculate the volume (in liters) of \(\mathrm{CO}_{2}\) generated from \(0.350 \mathrm{~g}\) of \(\mathrm{NaHCO}_{3}\) and excess gastric juice at \(1.00 \mathrm{~atm}\) and \(37.0^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The volume of carbon dioxide gas produced is 0.106 liters.

Step by step solution

01

Calculate moles of Sodium Bicarbonate

First, calculate the molar mass of \(NaHCO_3\). Adding up the atomic masses of Na (22.99 g/mol), H (1.01 g/mol), C (12.01 g/mol) and O (16.00 g/mol), we get 84.01 g/mol. Since we know the mass is 0.350 g, to get the number of moles we divide the mass by the molar mass. Number of moles = \(\frac{0.350}{84.01} = 0.00417\) moles.
02

Use stoichiometry

From the balanced chemical reaction, we know that one mole of sodium bicarbonate (\(NaHCO_3\)) reacts to generate one mole of carbon dioxide (\(CO_2\)). Therefore, number of moles of \(CO_2\) produced = number of moles of \(NaHCO_3\) = 0.00417 moles.
03

Use the ideal gas law

The ideal gas law is \(PV = nRT\), where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. We are given P = 1.00 atm, n = 0.00417 moles, R = 0.0821 L.atm/mol.k (standard value), and T = 37.0掳C which we need to convert to Kelvin by adding 273, T = 37.0 + 273 = 310 K. Solving for V, we have \(V = \frac{nRT}{P} = \frac{(0.00417 mol)(0.0821 L.atm/mol.k)(310 K)}{1.00 atm} = 0.106\) L.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Stoichiometry
Stoichiometry is like a recipe for chemical reactions. It helps us understand the relationships between reactants and products. When you bake cookies, you follow a recipe that tells you exactly how much of each ingredient you need. Similarly, in a chemical reaction, stoichiometry tells us how much of each substance is involved.

In the exercise, we used stoichiometry to find out how much carbon dioxide ( CO_2 ) is produced from a specific amount of sodium bicarbonate ( NaHCO_3 ).
  • The balanced chemical equation shows the ratio of the substances. Here, 1 mole of NaHCO_3 produces 1 mole of CO_2 .
  • By knowing the moles of NaHCO_3 , we could directly find the moles of CO_2 .
This is the magic of stoichiometry. It allows us to use known quantities to discover unknowns in a reaction.
Exploring Chemical Reactions
Chemical reactions are processes where substances, known as reactants, are transformed into different substances, called products. They involve breaking and forming bonds between atoms.

In our example, the reaction between antacid ( NaHCO_3 ) and hydrochloric acid ( HCl ) produces salt ( NaCl ), water ( H_2O ), and carbon dioxide ( CO_2 ).
  • Reactants: NaHCO_3 and HCl .
  • Products: NaCl , H_2O , and CO_2 .
This balanced equation ensures that the number of atoms for each element is the same on both sides. It's like maintaining a balance, where nothing is lost or gained, just rearranged.
Molar Mass Calculation Explained
Molar mass is a bridge between grams and moles. It鈥檚 the weight of one mole of a substance, measured in grams per mole (\text{g/mol}). Calculating molar mass involves adding up the atomic masses from the periodic table.

For sodium bicarbonate (NaHCO_3):
  • Sodium (Na) is 22.99 \text{g/mol}.
  • Hydrogen (H) is 1.01 \text{g/mol}.
  • Carbon (C) is 12.01 \text{g/mol}.
  • Oxygen (O) is 16.00 \text{g/mol} (there are three oxygens, so multiply by 3).
The total molar mass is 84.01 \text{g/mol}. This allows us to convert a given mass of a substance (like 0.350 g of NaHCO_3) into moles, using: \[\text{Number of moles} = \frac{\text{Mass}}{\text{Molar Mass}}\]. Understanding molar mass is essential for predicting and measuring amounts in chemical reactions.

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Most popular questions from this chapter

The \(\mathrm{pH}\) of an HF solution is 6.20 . Calculate the ratio [conjugate base]/[acid] for HF at this pH.

Hemoglobin (Hb) is a blood protein that is responsible for transporting oxygen. It can exist in the protonated form of \(\mathrm{HbH}^{+}\). The binding of oxygen can be represented by the simplified equation $$\mathrm{HbH}^{+}+\mathrm{O}_{2} \rightleftharpoons \mathrm{HbO}_{2}+\mathrm{H}^{+}$$ (a) What form of hemoglobin is favored in the lungs where oxygen concentration is highest? (b) In body tissues, where carbon dioxide is released as a result of metabolism, the medium is more acidic because of the formation of carbonic acid. What form of hemoglobin is favored under this condition? (c) When a person hyperventilates, the concentration of \(\mathrm{CO}_{2}\) in his or her blood decreases. How does this action affect the above equilibrium? Frequently a person who is hyperventilating is advised to breathe into a paper bag. Why does this action help the individual?

Which would be considered a stronger Lewis acid: (a) \(\mathrm{BF}_{3}\) or \(\mathrm{BCl}_{3},\) (b) \(\mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\) ? Explain.

Both the amide ion \(\left(\mathrm{NH}_{2}^{-}\right)\) and the nitride ion \(\left(\mathrm{N}^{3-}\right)\) are stronger bases than the hydroxide ion and hence do not exist in aqueous solutions. (a) Write the equations showing the reactions of these ions with water, and identify the Bronsted acid and base in each case. (b) Which of the two is the stronger base?

Define Bronsted acids and bases. How do the Bronsted definitions differ from Arrhenius's definitions of acids and bases?
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