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Chapter 2: Problem 38

Observations of the reaction between nitrogen gas and hydrogen gas show us that 1 volume of nitrogen reacts with 3 volumes of hydrogen to make 2 volumes of gaseous product, as shown below: Determine the formula of the product and justify your answer.

Short Answer

Expert verified
The formula of the product is \(NH_3\). This is determined by applying the law of combining volumes, using the given volume ratios of reactants and products, and finding the correct stoichiometry for nitrogen and hydrogen in the balanced chemical equation \(N_2 + 3H_2 \rightarrow 2NH_3\).

Step by step solution

01

Analyze the given reaction volume ratios

We know that 1 volume of nitrogen reacts with 3 volumes of hydrogen to make 2 volumes of gaseous product. The ratio of reactants and product is important to help us determine the stoichiometry of the reaction between nitrogen and hydrogen.
02

State the general reactions for nitrogen and hydrogen

We should state the general reactions of nitrogen and hydrogen gases reacting to form a gaseous product as follows: \(N_2 + xH_2 \rightarrow yNH_n\) In this general reaction, x and y are whole numbers that represent the coefficients for the hydrogen and product, respectively. The subscript n in NH_n represents the ratio of hydrogen atoms to nitrogen atoms in the product.
03

Apply the law of combining volumes

According to the law of combining volumes, the ratio of the gas volumes of reactants and products in a chemical reaction, when measured under the same conditions of temperature and pressure, corresponds to the stoichiometric coefficients of the gas components in the balanced chemical equation. In this case, the volume ratios are 1:3:2 for nitrogen, hydrogen, and the product, respectively. Therefore, we can rewrite the general reaction as follows: \(N_2 + 3H_2 \rightarrow 2NH_n\)
04

Determine the value of n

To determine the value of n, we should look at the number of hydrogen atoms on both sides of the balanced chemical equation. On the left side, we have 6 hydrogen atoms (from 3 moles of hydrogen gas, each with 2 hydrogen atoms). On the right side, we have 2 times n hydrogen atoms (from 2 moles of product, each with n hydrogen atoms). We can write this as an equation: \(6 = 2n\) Solve for n: \(n = 3\)
05

Write the formula of the product and justify the answer

Now that we've found the value of n to be 3, we can write the formula of the product as \(NH_3\). The balanced chemical equation for the reaction between nitrogen and hydrogen gases is as follows: \(N_2 + 3H_2 \rightarrow 2NH_3\) Since we've used the law of combining volumes to balance the chemical equation and determine the stoichiometry of the reaction between nitrogen and hydrogen, the formula of the gaseous product (\(NH_3\)) is justified.

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Most popular questions from this chapter

For each of the following ions, indicate the total number of protons and electrons in the ion. For the positive ions in the list, predict the formula of the simplest compound formed between each positive ion and the oxide ion. Name the compounds. For the negative ions in the list, predict the formula of the simplest compound formed between each negative ion and the aluminum ion. Name the compounds. a. \(\mathrm{Fe}^{2+}\) b. \(\mathrm{Fe}^{3+}\) c. \(\mathrm{Ba}^{2+}\) d. \(\mathrm{Cs}^{+}\) e. \(\mathrm{S}^{2-}\) f. \(\mathrm{P}^{3-}\) g. \(\mathrm{Br}^{-}\) h. \(\mathrm{N}^{3-}\)

Two elements, R and Q, combine to form two binary compounds. In the first compound, 14.0 g of R combines with 3.00 g of Q. In the second compound, 7.00 g of R combines with 4.50 g of Q. Show that these data are in accord with the law of multiple proportions. If the formula of the second compound is RQ, what is the formula of the first compound?

Explain the law of conservation of mass, the law of definite proportion, and the law of multiple proportions.

When mixtures of gaseous \(\mathrm{H}_{2}\) and gaseous \(\mathrm{Cl}_{2}\) react, a product forms that has the same properties regardless of the relative amounts of \(\mathrm{H}_{2}\) and \(\mathrm{Cl}_{2}\) used. a. How is this result interpreted in terms of the law of definite proportion? b. When a volume of \(\mathrm{H}_{2}\) reacts with an equal volume of \(\mathrm{Cl}_{2}\) at the same temperature and pressure, what volume of product having the formula HCl is formed?

Consider 100.0 -g samples of two different compounds consisting only of carbon and oxygen. One compound contains 27.2 \(\mathrm{g}\) of carbon, and the other has 42.9 \(\mathrm{g}\) of carbon. How can these data support the law of multiple proportions if 42.9 is not a multiple of 27.2\(?\) Show that these data support the law of multiple proportions.
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