Avogadro's hypothesis states that:
- A. Each atom of oxygen is 16 times more massive than an atom of hydrogen.
- B. A given compound always contains exactly the same proportion of elements by mass.
- C. When two elements form a series of compounds, the ratios of masses that combine with 1 gram of the first element can always be reduced to small whole numbers.
- D. At the same temperature and pressure, equal volumes of different gases contain an equal number of particles.
Correct Answer: D
Rationale: Rationale for correct answer D: Avogadro's hypothesis states that equal volumes of different gases at the same temperature and pressure contain an equal number of particles. This is because gases behave similarly under these conditions due to the ideal gas law. Avogadro's hypothesis is crucial in understanding the behavior of gases and is fundamental in the study of chemistry.
Summary of incorrect choices:
A: This statement is about the relative mass of atoms of different elements, not Avogadro's hypothesis.
B: This statement relates to the law of definite proportions, not Avogadro's hypothesis.
C: This statement refers to the law of multiple proportions, not Avogadro's hypothesis.
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You measure water in two containers: a 10-mL graduated cylinder with marks at every mL, and a 1-mL pipet marked at every 1 mL. If you have some water in each of the containers and add them together, to what decimal place could you report the total volume of water?
- A. 0.01 mL
- B. 0.1 mL
- C. 1 mL
- D. 10 mL
Correct Answer: C
Rationale: The correct answer is C: 1 mL. When adding volumes measured in different containers, you should report the result to the least precise measurement scale, which is the 1 mL pipet in this case. The graduated cylinder measures to the nearest mL, so the total volume should be rounded to the nearest whole mL. Reporting to a decimal place of 0.01 mL or 0.1 mL would imply a level of precision greater than what the equipment can provide. Choice D is incorrect as it exceeds the maximum volume capacity of the containers and is not relevant to the precision of the measurements.
How many significant figures are there in the number 0006428?
- A. 7
- B. 3
- C. 8
- D. 4
Correct Answer: D
Rationale: The correct answer is D: 4. Significant figures are non-zero digits and zeros between them. In this case, only digits 6, 4, 2, and 8 are non-zero, making them all significant. Zeros before the first non-zero digit are not significant, so the zeros before 6 are not counted. Hence, there are 4 significant figures in the number 0006428.
Choice A (7) is incorrect because it includes all digits, including the leading zeros, which are not significant. Choice B (3) is incorrect because it only considers the non-zero digits, excluding the zeros between them. Choice C (8) is incorrect because it counts all digits including leading zeros, which are not significant.
A 0 mL sample of glycerol has a mass of 2 grams. What is the mass of a 57-mL sample of glycerol?
- A. 8.8 g
- B. 45 g
- C. 2.9 104 g
- D. 72 g
Correct Answer: B
Rationale: To find the mass of a 57-mL sample of glycerol, we use the given mass-to-volume ratio. Since 0 mL has a mass of 2 grams, the mass-to-volume ratio is 2g/0mL = 2g/mL. Therefore, for a 57-mL sample, we multiply 2g/mL by 57 mL to get 114 grams, which corresponds to answer choice B.
Choice A (8.8 g) is incorrect because it does not align with the calculated mass of 114 g for a 57-mL sample. Choices C (2.9 104 g) and D (72 g) are also incorrect as they are not consistent with the mass-to-volume ratio of 2g/mL provided in the question.
Many classic experiments have given us indirect evidence of the nature of the atom. Which of the experiments listed below did not give the results described?
- A. The Rutherford experiment proved the Thomson "plum- pudding" model of the atom to be essentially correct.
- B. The Rutherford experiment was useful in determining the nuclear charge on the atom.
- C. Millikan's oil-drop experiment showed that the charge on any particle was a simple multiple of the charge on the electron.
- D. The electric discharge tube proved that electrons have a negative charge.
Correct Answer: A
Rationale: The correct answer is A because the Rutherford experiment actually disproved the Thomson "plum-pudding" model of the atom. Rutherford's experiment involved firing alpha particles at a thin gold foil and observing their scattering patterns. The results showed that atoms have a small, dense, positively charged nucleus, which contradicted the Thomson model. Choice B is correct as the experiment was indeed useful in determining the nuclear charge on the atom. Choice C is incorrect because Millikan's oil-drop experiment determined the charge on the electron, not just that it was a simple multiple. Choice D is incorrect as the electric discharge tube did show that electrons have a negative charge.
Consider the numbers 23.68 and 4.12. The sum of these numbers has
significant figures, and the product of these numbers has _
significant figures.
- A. 3, 3
- B. 4, 4
- C. 3, 4
- D. 4, 3
Correct Answer: D
Rationale: To determine the significant figures in the sum of 23.68 and 4.12, we add the numbers which results in 27.8. The sum has 3 significant figures because the least precise number has 2 decimal places.
To find the significant figures in the product, we multiply the numbers which equals 97.4096. The product has 4 significant figures since the number with the fewest significant figures has 2 before the decimal point and 4 after.
Therefore, the correct answer is D (4 significant figures in the product and 3 in the sum).