A radioactive isotope has a half-life of 20 years. How many grams of a 6-gram sample will remain after 40 years?

Correct Answer: C

Rationale: The half-life of a radioactive isotope is the time it takes for half of the original sample to decay. After each half-life period, half of the initial sample remains. In this case, after the first 20 years, half of the 6-gram sample (3 grams) will remain. After another 20 years (total of 40 years), half of the remaining 3 grams will remain, which is 1.5 grams. Therefore, 3 grams will be left after 40 years. Choice A is incorrect as it doesn't consider the concept of half-life and incorrectly suggests an increase in the sample. Choice B is incorrect as it assumes no decay over time. Choice D is incorrect as it miscalculates the remaining amount after two half-life periods.

Correct Answer: C

Rationale: The reaction shown (8Fe + S → 8FeS) is a synthesis reaction. In a synthesis reaction, two or more substances combine to form a single compound. In this case, iron (Fe) and sulfur (S) combine to form iron sulfide (FeS). The key characteristic of a synthesis reaction is the formation of a single product from multiple reactants, which aligns with the given chemical equation. Choice A, single displacement, involves an element displacing another in a compound, which is not the case here. Choice B, double displacement, involves the exchange of ions between two compounds, which is also not happening in this reaction. Choice D, acid-base, refers to reactions between an acid and a base to form salt and water, which is not the case in the given equation.

Correct Answer: A

Rationale: In the solid state, you would expect a nonmetal to be brittle. Nonmetals generally lack the malleability and ductility of metals, which makes them prone to being brittle and easily fractured under stress. This property is due to the lack of metallic bonding in nonmetals, which results in a more rigid and less flexible structure. Choice B, 'lustrous,' is incorrect because nonmetals typically do not exhibit a shiny or reflective surface like metals do. Choice C, 'malleable,' is also incorrect as nonmetals lack the ability to be hammered or rolled into thin sheets like metals. Choice D, 'conductive,' is incorrect since nonmetals are generally poor conductors of electricity compared to metals.

Correct Answer: B

Rationale: The rate of diffusion is inversely proportional to the molar mass of the gas. Helium has the lowest molar mass among the given gases, making it the lightest and fastest gas to diffuse. Therefore, helium would be expected to diffuse most rapidly compared to carbon monoxide, nitrogen, and oxygen. Carbon monoxide, nitrogen, and oxygen have higher molar masses than helium, so they would diffuse more slowly. Therefore, the correct answer is helium.

Correct Answer: A

Rationale: Ozone (O3) is a triatomic allotrope of oxygen. It differs from the common diatomic oxygen molecule (O2) by having three oxygen atoms bonded together. Ozone is known for its protective role in the Earth's atmosphere, absorbing most of the Sun's harmful ultraviolet radiation. Water (H2O) is a compound composed of two hydrogen atoms and one oxygen atom. Acidic oxide and carbon dioxide are not triatomic allotropes of oxygen. Carbon dioxide consists of one carbon atom and two oxygen atoms, while acidic oxides refer to compounds where oxygen is bonded with other elements to form oxides, and they are not allotropes of oxygen.