Which of the following relations is a mathematical expression of Charles' law?

Here are the answers to the multiple-choice questions: 38. Which of the following substances would liberate hydrogen at its melting point? Calcium hydride (CaH_2) is a metal hydride. While its primary use for hydrogen generation is reaction with water, metal hydrides can decompose at high temperatures to liberate hydrogen. The melting point of CaH_2 is 816°C, at which temperature thermal decomposition to calcium and hydrogen gas is possible. Other options like water, sodium hydroxide, and formic acid do not liberate hydrogen at their respective melting points. The correct answer is C. CaH_2. 39. Which of these functional groups is not commonly found in proteins? Proteins are polymers of amino acids. Amino acids contain amino (-NH_2) and carboxyl (-COOH) functional groups. When amino acids link, they form peptide bonds, which are amide (-CONH-) functional groups. Many amino acid side chains contain alcohol (-OH) functional groups (e.g., serine, threonine). While the carboxyl group is present in proteins (at the C-terminus and in acidic side chains), "alkanoic acids" refers to a class of compounds (R-COOH) rather than a specific functional group type commonly found within the protein chain in the same way as amine, amide, or alcohol groups. The correct answer is D. Alkanoic acids. 40. The brown ring test is used to determine the presence of The brown ring test is a chemical test used to detect the presence of nitrate ions (NO_3^-) in a solution. The correct answer is D. NO_3^-. 41. Which of the following relations is a mathematical expression of Charles' law? Charles's Law states that for a fixed mass of gas at constant pressure, the volume (V) is directly proportional to its absolute temperature (T). This can be expressed as (V)/(T) = constant or, for two different states, (V_1)/(T_1) = (V_2)/(T_2). The correct answer is C. (V_1)/(T_1) = (V_2)/(T_2). 42. Which of the following substances has its solubility decreasing with increasing temperature? The solubility of most solid substances in water increases with increasing temperature. However, the solubility of gases in liquids (like water) generally decreases as the temperature increases. Carbon dioxide (CO_2) is a gas. The correct answer is B. CO_2. 43. The quantity of electricity required to discharge 1 mole of univalent ions is A univalent ion has a charge of +1 or -1. To discharge 1 mole of univalent ions, 1 mole of electrons is required. The charge carried by 1 mole of electrons is known as Faraday's constant, which is approximately 96,500 coulombs (C). The correct answer is B. 96,500 C. 44. The delocalized electrons present in metals are responsible for which of the following properties of metals? Metals have a "sea" of delocalized electrons that are free to move throughout the metallic lattice. This free movement of electrons is responsible for the high electrical conductivity of metals. The correct answer is C. Electrical conductivity. 45. One of the allotropes of carbon is Allotropes are different structural forms of the same element. Diamond is a well-known allotrope of carbon, along with graphite and fullerenes. Gold, mercury, and silver are other metallic elements, not allotropes of carbon. The correct answer is B. diamond. 46. When water vapour condenses to form liquid water, it Condensation is a phase transition from a gas (water vapor) to a liquid (liquid water). This process involves the release of energy (heat) as the water molecules slow down and form stronger intermolecular bonds. Therefore, condensation is an exothermic process. The correct answer is D. releases heat. Drop the next question.