If fifty-six kilograms of a radioactive substance has a half-life of 12 days, how many days will it take the substance to decay naturally to only 7 kilograms?

Correct Answer: C

Rationale: To decay from 56 kg to 7 kg, the substance needs to go through 3 half-lives (56 kg · 2 · 2 · 2 = 7 kg). Since each half-life is 12 days, the total time required is 12 days per half-life x 3 half-lives = 36 days. Choice A is incorrect because it does not consider the concept of half-lives. Choice B is incorrect because it represents the duration of a single half-life, not the total time required for the decay. Choice D is incorrect as it does not account for the multiple half-lives needed for the substance to decay from 56 kg to 7 kg.

Correct Answer: B

Rationale: The chemical equation AB → A + B represents a decomposition reaction. In a decomposition reaction, a single compound breaks down into two or more simpler substances. In this specific reaction, compound AB is decomposed into its elements, A and B, making it a decomposition reaction. Choice A, Synthesis, involves the combination of two or more substances to form a more complex product, which is not the case here. Choices C and D, Single replacement and Double replacement, involve the exchange of ions between compounds or elements, which is not happening in the given reaction.

Correct Answer: C

Rationale: Sulfur is a nonmetal as it is located on the right side of the periodic table. Nonmetals generally exhibit properties such as being brittle, poor conductors of heat and electricity, and having lower melting points compared to metals. Mercury (A), Magnesium (B), and Potassium (D) are all metals due to their metallic properties. Mercury is a liquid metal at room temperature, Magnesium is a solid metal, and Potassium is a solid metal as well. Therefore, the correct answer is C, Sulfur.

Correct Answer: A

Rationale: The rate of effusion of a gas is inversely proportional to the square root of its molar mass. Since Gas A has twice the mass of Gas B, Gas A will effuse more slowly than Gas B. Therefore, you will likely smell Gas A before you smell Gas B as Gas A will escape and diffuse through the porous plug at a slower rate compared to Gas B. Choice A is correct because Gas A, with its higher molar mass, will take longer to effuse through the porous plug, causing you to smell it first. Choices B, C, and D are incorrect as they do not consider the relationship between molar mass and effusion rate.

Correct Answer: C

Rationale: The three important allotropic forms of phosphorus are red, white, and black. These forms indicate the different physical properties and reactivity of phosphorus under various conditions. Red phosphorus is more stable and less reactive than white phosphorus, while black phosphorus is the least reactive form. Choice C, 'black,' is the correct answer as it completes the sequence of allotropic forms of phosphorus. Choices A, 'green,' B, 'gray,' and D, 'silver,' are incorrect as they do not represent recognized forms of phosphorus.