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Chapter 9: Problem 86

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 zine is reacted with excess aqueous hydrochloric acid?

Short Answer

Expert verified
When \(2.50 \ \text{g}\) of zinc reacts with excess aqueous hydrochloric acid, \(0.0771 \ \text{g}\) of hydrogen gas is produced.

Step by step solution

01

Determine the molar mass of the substances involved#important# In order to perform stoichiometric calculations, we need to know the molar mass of zinc and hydrogen: - Molar mass of zinc (Zn): 65.38 g/mol - Molar mass of hydrogen (H鈧�): 2.02 g/mol

Step 2: Calculate moles of zinc reacted#important# To find the moles of zinc reacted, we can use the given mass (2.50 g) and the molar mass of zinc (65.38 g/mol): $$ \text{moles of Zn} = \frac{\text{mass of Zn}}{\text{molar mass of Zn}} = \frac{2.50 \ \text{g}}{65.38 \ \text{g/mol}} = 0.0382 \ \text{mol} $$
02

Calculate moles of hydrogen produced#important# The stoichiometric ratio between Zn and H鈧� from the balanced equation is 1:1. Therefore, the moles of hydrogen produced would be the same as the moles of zinc reacted: $$ \text{moles of H鈧倉 = \text{moles of Zn} = 0.0382 \ \text{mol} $$

Step 4: Calculate mass of hydrogen produced#important# Finally, we can calculate the mass of hydrogen gas produced by using the calculated moles of hydrogen and its molar mass (2.02 g/mol): $$ \text{mass of H鈧倉 = \text{moles of H鈧倉 \times \text{molar mass of H鈧倉 = 0.0382 \ \text{mol} \times 2.02 \ \text{g/mol} = 0.0771 \ \text{g} $$ So, when 2.50 g of zinc reacts with excess aqueous hydrochloric acid, 0.0771 g of hydrogen gas is produced.

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Key Concepts

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

Chemical Reactions
Chemical reactions describe the process by which substances interact and transform into new products. In this exercise, the reaction involves zinc (Zn) and hydrochloric acid (HCl). This is a single displacement reaction, a type where an element displaces another in a compound, leading to the formation of a new product.
  • Zinc, a metal, and hydrochloric acid, an aqueous solution, react to form zinc chloride (ZnCl2) and hydrogen gas (H2).
  • The balanced chemical equation for this reaction is: \( \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) \).
Chemical reactions like this one can be explored further using stoichiometry, which helps in predicting the amounts of products formed and reactants consumed.
Molar Mass Calculation
Molar mass is fundamental in stoichiometry, converting between mass and moles. It's the mass of one mole of a substance, expressed in grams per mole (g/mol). This concept is used to relate the mass of a chemical substance to the quantity in moles.
  • To calculate the molar mass of zinc, we use its atomic mass of 65.38 g/mol.
  • For hydrogen gas (H2), with two hydrogen atoms, its molar mass is 2.02 g/mol.
The calculation of moles from mass involves the equation: \[\text{moles} = \frac{\text{mass of substance}}{\text{molar mass}}\]This conversion is critical in predicting product amounts by using the balanced reaction equation as a guide.
Hydrogen Gas Production
In this type of reaction, understanding how to calculate and predict hydrogen gas yield is crucial. Producing hydrogen gas involves using metals like zinc reacting with acids, which is a common laboratory practice.
  • Starting with 2.50 g of zinc, we determine moles using its molar mass: \( 0.0382 \text{ mol of Zn} \).
  • The stoichiometry of the reaction shows a 1:1 mole ratio between zinc and hydrogen gas.
  • This means the moles of hydrogen gas produced equals the moles of zinc reacted: \( 0.0382 \text{ mol of H}_2 \).
  • Finally, converting moles of hydrogen to mass involves multiplying by the molar mass of hydrogen, resulting in 0.0771 g of hydrogen gas.
Such calculations underline the importance of understanding stoichiometry and reactions to estimate gas production efficiently.

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Most popular questions from this chapter

Using the average atomic masses given inside the front cover of this book, calculate the mass in grams of each of the following samples. a. 2.17 moles of germanium, Ge b. \(4.24 \mathrm{mmol}\) of lead(II) chloride ( \(1 \mathrm{mmol}=1 / 1000 \mathrm{~mol}\) ) c. 0.0971 mole of ammonia, \(\mathrm{NH}_{3}\) d. \(4.26 \times 10^{3}\) moles of hexane, \(\mathrm{C}_{6} \mathrm{H}_{14}\) e. 1.71 moles of iodine monochloride, \(1 \mathrm{C}=\)

Natural waters often contain relatively high levels of calcium ion, \(\mathrm{Ca}^{2+},\) and hydrogen carbonate ion (bicarbonate), \(\mathrm{HCO}_{3}^{-}\), from the leaching of minerals into the water. When such water is used commercially or in the home, heating of the water leads to the formation of solid calcium carbonate, \(\mathrm{CaCO}_{3}\), which forms a deposit ("scale") on the interior of boilers, pipes, and other plumbing fixtures. $$ \mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}(a q) \rightarrow \mathrm{CaCO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) $$ If a sample of well water contains \(2.0 \times 10^{-3} \mathrm{mg}\) of \(\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}\) per milliliter, what mass of \(\mathrm{CaCO}_{3}\) scale would \(1.0 \mathrm{~mL}\) of this water be capable of depositing?

Many metals occur naturally as sulfide compounds, examples include \(\mathrm{ZnS}\) and \(\mathrm{CoS}\). Air pollution often accompanies the processing of these ores, because toxic sulfur dioxide is released as the ore is converted from the sulfide to the oxide by roasting (smelting). For example, consider the unbalanced equation for the roasting reaction for zinc: $$ \mathrm{ZnS}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{ZnO}(s)+\mathrm{SO}_{2}(g) $$ How many kilograms of sulfur dioxide are produced when \(1.0 \times 10^{2} \mathrm{~kg}\) of \(\mathrm{ZnS}\) is roasted in excess oxygen by this process?

Using the average atomic masses given inside the front cover of this book, calculate the mass in grams of each of the following samples. a. 0.341 mole of potassium nitride b. \(2.62 \mathrm{mmol}\) of neon \((1 \mathrm{mmol}=1 / 1000 \mathrm{~mol})\) c. 0.00449 mole of manganese(II) oxide d. \(7.18 \times 10^{5}\) moles of silicon dioxide e. 0.000121 mole of iron( III) phosphate

Over the ycars, the thermite reaction has been used for welding railroad rails, in incendiary bombs, and to ignite solid fuel rocket motors. The reaction is $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \rightarrow 2 \mathrm{Fe}(l)+\mathrm{Al}_{2} \mathrm{O}_{3}(s) $$ What mass of iron(III) oxide must be used to produce \(25.69 \mathrm{~g}\) of iron? b. What mass of aluminum must be used to produce \(25.69 \mathrm{~g}\) of iron? c. What is the maximum mass of aluminum oxide that could be produced along with \(25.69 \mathrm{~g}\) of iron?
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