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Solutions of sodium hydroxide cannot be kept for very long because they absorb carbon dioxide from the air, forming sodium carbonate. The unbalanced equation is $$\mathrm{NaOH}(a q)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$$ Calculate the number of grams of carbon dioxide that can be absorbed by complete reaction with a solution that contains \(5.00 \mathrm{g}\) of sodium hydroxide.

Short Answer

Expert verified
The complete reaction with a solution that contains 5.00 grams of sodium hydroxide can absorb 2.75 grams of carbon dioxide.

Step by step solution

01

Balance the chemical equation

To balance the chemical equation, we need to make sure that the number of atoms for each element is the same on both sides of the equation. After examining the equation, it can be balanced by adding a coefficient of 2 in front of NaOH: $$2 \mathrm{NaOH}(a q)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$$ Now the equation is balanced.
02

Convert grams of NaOH to moles

We are given 5.00 grams of sodium hydroxide (NaOH). The molecular weight of NaOH is approximately: Na = 22.99 g/mol O = 16.00 g/mol H = 1.01 g/mol Molecular weight of NaOH = (22.99 + 16.00 + 1.01) g/mol = 40.00 g/mol Now we will convert grams of NaOH to moles using its molecular weight: moles of NaOH = (5.00 g) / (40.00 g/mol) = 0.125 mol
03

Use the balanced equation to convert moles of NaOH to moles of COâ‚‚

The balanced equation shows that 2 moles of NaOH react with 1 mole of COâ‚‚. We have 0.125 moles of NaOH, so we can set up a proportion to determine how many moles of COâ‚‚ can react: \(\frac{0.125 \text{ mol NaOH}}{x \text{ mol CO}_{2}} = \frac{2 \text{ mol NaOH}}{1 \text{ mol CO}_{2}}\) Solving for x, we get: x = \(\frac{0.125 \text{ mol NaOH}}{2}\) = 0.0625 mol COâ‚‚
04

Convert moles of COâ‚‚ back to grams

To find the mass of COâ‚‚ that can be absorbed, we will convert 0.0625 mol COâ‚‚ back to grams using its molecular weight. The molecular weight of COâ‚‚ is approximately: C = 12.01 g/mol O = 16.00 g/mol (2 oxygens, so multiply by 2) Molecular weight of COâ‚‚ = (12.01 + 2 * 16.00) g/mol = 44.01 g/mol grams of COâ‚‚ = (0.0625 mol) * (44.01 g/mol) = 2.75 g So, the complete reaction with a solution that contains 5.00 grams of sodium hydroxide can absorb 2.75 grams of carbon dioxide.

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Key Concepts

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

Balancing Chemical Equations
Balancing chemical equations is a crucial step in accurately representing a chemical reaction. An unbalanced equation has unequal numbers of atoms for each element on both sides. To balance the equation for the reaction of sodium hydroxide (NaOH) with carbon dioxide (COâ‚‚), we aim to have the same number of each type of atom on both sides of the reaction. Initially, we have the equation:
  • NaOH + COâ‚‚ → Naâ‚‚CO₃ + Hâ‚‚O
Upon examination, to balance the equation, we add a coefficient of 2 in front of NaOH:
  • 2 NaOH + COâ‚‚ → Naâ‚‚CO₃ + Hâ‚‚O
Now, there are 2 sodium (Na) atoms, 2 oxygen (O) atoms from NaOH on the reactant side, and 3 oxygen (O) atoms, 1 carbon (C) atom, and 2 hydrogen (H) atoms on the product side. By ensuring both sides have an equal count for all atoms, the equation becomes balanced, facilitating further calculations of the reaction.
Stoichiometry
Stoichiometry involves using the relationships between reactants and products in a chemical equation to perform calculations. It allows us to determine the amount of substances involved in reactions. In our equation for the reaction of 2NaOH and COâ‚‚, stoichiometry helps us find out how much carbon dioxide is absorbed. Once the equation is balanced, the ratios derived offer a direct path to calculation:
  • For every 2 moles of NaOH, 1 mole of COâ‚‚ is needed.
This proportion is essential for determining quantities in a chemical reaction, as seen in conversions from moles of one substance to moles of another. It allows us to calculate how much of each reactant is consumed and how much product is formed.
Mole Calculations
Mole calculations help convert between masses and moles, facilitating a deeper understanding of chemical reactions. This is particularly important in reactions like the one between sodium hydroxide and carbon dioxide, where calculating moles is a necessity for creating a balanced equation. With a given amount of sodium hydroxide (5.00 g), we convert it to moles using its molecular weight:
  • Molecular weight of NaOH = 40.00 g/mol
  • Moles of NaOH = 5.00 g / 40.00 g/mol = 0.125 mol
By applying mole ratios from the balanced equation, we can then find the moles of carbon dioxide (COâ‚‚) absorbed. According to the ratio in the balanced equation, 2 moles of NaOH react with 1 mole of COâ‚‚:
  • Moles of COâ‚‚ = 0.125 mol NaOH × ( (1 mol COâ‚‚ / 2 mol NaOH) = 0.0625 mol COâ‚‚ )
Finally, using the molecular weight of COâ‚‚ (44.01 g/mol), we determine its mass in the reaction:
  • Grams of COâ‚‚ = 0.0625 mol × 44.01 g/mol = 2.75 g
These calculations bridge the molecular world and the observable, facilitating comprehensive chemical insights.
Chemical Absorption
Chemical absorption is the process where one substance is taken into another; here, it's about how sodium hydroxide solution absorbs carbon dioxide from the air. This is significant because it alters the chemical composition, forming sodium carbonate and water as products. The equation:
  • 2 NaOH + COâ‚‚ → Naâ‚‚CO₃ + Hâ‚‚O
illustrates that sodium hydroxide reacts with carbon dioxide to absorb 2.75 grams of COâ‚‚ for every 5 grams of NaOH. Understanding absorption is crucial for practical applications, such as purifying air or designing materials that capture airborne pollutants. This reaction shows that chemical absorption results in the transformation of the reactants into different products, demonstrating the reactive nature of chemical compounds when exposed to new environments.

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Most popular questions from this chapter

For each of the following balanced chemical equations, calculate how many moles and how many grams of each product would be produced by the complete conversion of 0.50 mol of the reactant indicated in boldface. State clearly the mole ratio used for each conversion. a. \(\mathbf{N} \mathbf{H}_{3}(g)+\mathrm{HCl}(g) \rightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\) b. \(\mathrm{CH}_{4}(g)+\mathbf{4} \mathbf{S}(s) \rightarrow \mathrm{CS}_{2}(l)+2 \mathrm{H}_{2} \mathrm{S}(g)\) c. \(\mathbf{P C I}_{3}+3 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{3} \mathrm{PO}_{3}(a q)+3 \mathrm{HCl}(a q)\) d. \(\mathbf{N a O H}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{NaHCO}_{3}(s)\)

Alkali metal hydroxides are sometimes used to "scrub" excess carbon dioxide from the air in closed spaces (such as submarines and spacecraft). For example, lithium hydroxide reacts with carbon dioxide according to the unbalanced chemical equation $$\mathrm{LiOH}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{Li}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)$$ Suppose a lithium hydroxide canister contains \(155 \mathrm{g}\) of \(\operatorname{LiOH}(s) .\) What mass of \(\mathrm{CO}_{2}(g)\) will the canister be able to absorb? If it is found that after 24 hours of use the canister has absorbed \(102 \mathrm{g}\) of carbondioxide, what percentage of its capacity has been reached?

When small quantities of elemental hydrogen gas are needed for laboratory work, the hydrogen is often generated by chemical reaction of a metal with acid. For example, zinc reacts with hydrochloric acid, releasing gaseous elemental hydrogen: $$\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)$$ What mass of hydrogen gas is produced when \(2.50 \mathrm{g}\) of zinc is reacted with excess aqueous hydrochloric acid?

The compound sodium thiosulfate pentahydrate, \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O},\) is important commercially to the photography business as "hypo," because it has the ability to dissolve unreacted silver salts from photographic film during development. Sodium thiosulfate pentahydrate can be produced by boiling elemental sulfur in an aqueous solution of sodium sulfite. $$\mathrm{S}_{8}(s)+\mathrm{Na}_{2} \mathrm{SO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s)$$ (unbalanced) What is the theoretical yield of sodium thiosulfate pentahydrate when \(3.25 \mathrm{g}\) of sulfur is boiled with 13.1 g of sodium sulfite? Sodium thiosulfate pentahydrate is very soluble in water. What is the percent yield of the synthesis if a student doing this experiment is able to isolate (collect) only \(5.26 \mathrm{g}\) of the product?

For each of the following unbalanced equations, indicate how many moles of the second reactant would be required to react exactly with 0.275 mol of the first reactant. State clearly the mole ratio used for the conversion. a. \(\mathrm{Cl}_{2}(g)+\mathrm{KI}(a q) \rightarrow \mathrm{I}_{2}(s)+\mathrm{KCl}(a q)\) b. \(\operatorname{Co}(s)+P_{4}(s) \rightarrow \operatorname{Co}_{3} P_{2}(s)\) c. \(\mathrm{Zn}(s)+\mathrm{HNO}_{3}(a q) \rightarrow \mathrm{ZnNO}_{3}(a q)+\mathrm{H}_{2}(g)\) d. \(C_{5} H_{12}(l)+O_{2}(g) \rightarrow C O_{2}(g)+H_{2} O(g)\)

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