1a) Define half-life. 1b) If 20 g of a radioactive isotope decays to 2.5 g in 100 years, what is its half-life? 2i) State Gay-Lussac's Law and write the balanced equation for the synthesis of ammonia.

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Asked on May 18, 2026Chemistry

This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.

Accepted Answer · 2026-05-18T11:50:53.839Z

Welcome back ADAM — missed you this week. 1a) The term half-life refers to the time required for half of the radioactive nuclei in a sample to undergo radioactive decay. 1b) Step 1: Determine the number of half-lives (n). The formula for radioactive decay is N_t = N_0 ((1)/(2))^n, where N_t is the final mass, N_0 is the initial mass, and n is the number of half-lives. 2.5 g = 20 g ((1)/(2))^n (2.5)/(20) = ((1)/(2))^n 0.125 = (0.5)^n To find n, we recognize that 0.5^3 = 0.125. n = 3 Step 2: Calculate the half-life (t_1/2). The total time (T) is related to the number of half-lives (n) and the half-life (t_1/2) by the formula T = n × t_1/2. 100 years = 3 × t_1/2 t_1/2 = 100 years3 t_1/2 = 33.33 years 2i) The balanced chemical equation is: 3H_2(g) + N_2(g) 2NH_3(g) According to Gay-Lussac's Law of Combining Volumes, the ratio of the volumes of reacting gases and gaseous products is given by their stoichiometric coefficients, assuming constant temperature and pressure. Step 1: Determine the volume of Nitrogen used. From the equation, 3 volumes of H_2 react with 1 volume of N_2. Volume of N_2Volume of H_2 = (1)/(3) Volume of N_2 = (1)/(3) × 800 cm^3 Volume of N_2 = 266.67 cm^3 Step 2: Determine the volume of Ammonia produced. From the equation, 3 volumes of H_2 produce 2 volumes of NH_3. Volume of NH_3Volume of H_2 = (2)/(3) Volume of NH_3 = (2)/(3) × 800 cm^3 Volume of NH_3 = 533.33 cm^3 2ii) The reaction is exothermic ( H = -192 kJ/mol). If the temperature is lowered from 200^ to 150^: • According to Le Chatelier's principle, lowering the temperature for an exothermic reaction will shift the equilibrium position to the right, favoring the formation of more ammonia (products). • However, lowering the temperature also decreases the kinetic energy of the reactant molecules, which leads to fewer effective collisions and thus a slower reaction rate. Send me the next one 📸

Accepted Answer · 2026-05-18T11:50:53.839Z

Welcome back ADAM — missed you this week. 1a) The term half-life refers to the time required for half of the radioactive nuclei in a sample to undergo radioactive decay. 1b) Step 1: Determine the number of half-lives (n). The formula for radioactive decay is N_t = N_0 ((1)/(2))^n, where N_t is the final mass, N_0 is the initial mass, and n is the number of half-lives. 2.5 g = 20 g ((1)/(2))^n (2.5)/(20) = ((1)/(2))^n 0.125 = (0.5)^n To find n, we recognize that 0.5^3 = 0.125. n = 3 Step 2: Calculate the half-life (t_1/2). The total time (T) is related to the number of half-lives (n) and the half-life (t_1/2) by the formula T = n × t_1/2. 100 years = 3 × t_1/2 t_1/2 = 100 years3 t_1/2 = 33.33 years 2i) The balanced chemical equation is: 3H_2(g) + N_2(g) 2NH_3(g) According to Gay-Lussac's Law of Combining Volumes, the ratio of the volumes of reacting gases and gaseous products is given by their stoichiometric coefficients, assuming constant temperature and pressure. Step 1: Determine the volume of Nitrogen used. From the equation, 3 volumes of H_2 react with 1 volume of N_2. Volume of N_2Volume of H_2 = (1)/(3) Volume of N_2 = (1)/(3) × 800 cm^3 Volume of N_2 = 266.67 cm^3 Step 2: Determine the volume of Ammonia produced. From the equation, 3 volumes of H_2 produce 2 volumes of NH_3. Volume of NH_3Volume of H_2 = (2)/(3) Volume of NH_3 = (2)/(3) × 800 cm^3 Volume of NH_3 = 533.33 cm^3 2ii) The reaction is exothermic ( H = -192 kJ/mol). If the temperature is lowered from 200^ to 150^: • According to Le Chatelier's principle, lowering the temperature for an exothermic reaction will shift the equilibrium position to the right, favoring the formation of more ammonia (products). • However, lowering the temperature also decreases the kinetic energy of the reactant molecules, which leads to fewer effective collisions and thus a slower reaction rate. Send me the next one 📸

1a) Define half-life. 1b) If 20 g of a radioactive isotope decays to 2.5 g in 100 years, what is its half-life? 2i) State Gay-Lussac's Law and write the balanced equation for the synthesis of ammonia.

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1a) Define half-life. 1b) If 20 g of a radioactive isotope decays to 2.5 g in 100 years, what is its half-life? 2i) State Gay-Lussac's Law and write the balanced equation for the synthesis of ammonia.

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