Laws of chemical combination

The governing concept is the law of multiple proportions. When the same fixed mass of one element combines with different masses of another element to form different compounds, those different masses should be compared and expressed in a simple whole-number ratio. Here, 12 g of A is constant in both compounds, so only the corresponding masses of B are compared: 18:30. The greatest common divisor of 18 and 30 is 6. Dividing both terms by 6 gives 18 ÷ 6 : 30 ÷ 6 = 3:5. Therefore, option A is correct. Option D is the original, unsimplified ratio; option C incorrectly compares A with B; and option B reverses the order of the two compounds.

This question applies the law of multiple proportions. The mass of A is kept constant at 30 g in both compounds, so the relevant comparison is between the two masses of B, namely 24 g and 96 g. Their ratio in the stated order is 24:96. The greatest common divisor of these two numbers is 24, so divide each term by 24: 24 ÷ 24 : 96 ÷ 24 = 1:4. Thus option B is correct. Option D shows the correct initial data but leaves the ratio unreduced. Option C compares the fixed mass of A with one mass of B, which is not what is asked. Option A reverses the order and gives 4:1 instead of 1:4.

The direct answer is C: 2:1:3. A ratio compares quantities in the order in which they are given. The volumes are 14 L, 7 L and 21 L, so begin with 14:7:21. To obtain the simplest ratio, divide every term by their greatest common divisor, 7: 14 ÷ 7 = 2, 7 ÷ 7 = 1, and 21 ÷ 7 = 3. Thus the ratio is 2:1:3. Option A is the unsimplified ratio, so it is numerically equivalent but not the simplest form. Option B changes the values incorrectly and gives 3:1:2. Option C follows the calculation exactly. Option D reverses the order and gives 1:2:3, which does not match the original order. Exam cue: divide every term by the same greatest common factor.

The direct answer is D: 2:3:1. Keep the three volumes in their given order: 16:24:8. The greatest common divisor of 16, 24 and 8 is 8. Divide each term by 8: 16 ÷ 8 = 2, 24 ÷ 8 = 3, and 8 ÷ 8 = 1. Therefore the simplest ratio is 2:3:1. Option A repeats the original values and does not simplify them. Option B, 1:3:2, is wrong because it changes the relative order and values. Option C, 1:2:3, also does not represent these three volumes in the given order. Option D is correct because multiplying 2:3:1 by 8 returns 16:24:8. Same temperature and pressure are relevant to comparing gas volumes, but the actual question here is simply ratio simplification. Remember: never divide only one term.

The direct answer is A: 3:1:2. Write the values in order as 18:6:12. The greatest common divisor is 6. Dividing term by term gives 18 ÷ 6 = 3, 6 ÷ 6 = 1, and 12 ÷ 6 = 2. Hence the simplest ratio is 3:1:2. Option A is correct because it is exactly this reduced ratio. Option B, 18:6:12, is only the original unsimplified ratio, so it is not the requested simplest form. Option C, 2:1:3, wrongly changes the first and third relationships. Option D, 1:2:3, also does not follow from division by one common factor and reverses the relative sizes. A valid simplification must multiply back to the original numbers using one common factor; 3:1:2 multiplied by 6 gives 18:6:12. Memory cue: find the common divisor first.

The direct answer is B: 2:3:1. Preserve the order of the given volumes, so start with 20:30:10. Their greatest common divisor is 10. Divide all three terms by 10: 20 ÷ 10 = 2, 30 ÷ 10 = 3, and 10 ÷ 10 = 1. The simplest ratio is therefore 2:3:1. Option A is the original ratio and has not been reduced. Option B is correct because every term has been divided by the same factor and no further common divisor greater than 1 remains. Option C, 1:3:2, changes the relationships between the quantities. Option D, 1:2:3, also reverses the size pattern and cannot be obtained by one common division. The units cancel in a ratio, but the order must remain fixed. Exam tip: check both simplification and order.

The direct answer is C: 1:3:2. Put the volumes in the given order: 9:27:18. The greatest common divisor is 9. Divide each term by 9: 9 ÷ 9 = 1, 27 ÷ 9 = 3, and 18 ÷ 9 = 2. Therefore the simplest ratio is 1:3:2. Option A, 9:27:18, is correct as an equivalent ratio but not in simplest form. Option B, 2:3:1, gives a different order and different relationships. Option C is correct because it comes directly from common division. Option D, 1:2:3, would incorrectly make the second volume twice the first and the third three times the first; actually the second is three times the first and the third twice the first. The condition of equal temperature and pressure does not change the arithmetic. Memory cue: compare each volume with the first after dividing by the common factor.

The direct answer is D: 1:2:3. The given ratio is 11:22:33. The greatest common divisor of all three numbers is 11. Divide each term by 11: 11 ÷ 11 = 1, 22 ÷ 11 = 2, and 33 ÷ 11 = 3. Thus the simplest ratio is 1:2:3. Option A is the unsimplified original ratio. Option B, 3:2:1, reverses the order and is not equivalent to the given ratio. Option C, 1:6:1, does not preserve the original relationships. Option D is correct because multiplying it by 11 reproduces 11:22:33 exactly. A ratio is simplified by dividing every term by the same common factor, never by changing the order or dividing terms by different numbers. Exam cue: when all values are multiples of the smallest value, divide by that value.

The direct answer is A: 1:2:1. Start with the volumes in order: 13:26:13. Their greatest common divisor is 13. Dividing all terms by 13 gives 13 ÷ 13 = 1, 26 ÷ 13 = 2, and 13 ÷ 13 = 1. Therefore the simplest ratio is 1:2:1. Option A is correct and is already in lowest terms because 1, 2 and 1 have no common divisor greater than 1. Option B, 13:26:13, is the original unsimplified ratio. Option C, 1:2:3, incorrectly changes the third volume; the third is equal to the first, not three times it. Option D, 1:6:1, incorrectly changes the middle volume; it is twice the first, not six times it. Check by multiplying 1:2:1 by 13 to recover the original volumes. Memory cue: equal original values remain equal after simplification.

The direct answer is B: 3:5:1. Keep the order of the volumes: 15:25:5. The greatest common divisor is 5. Divide each term by 5: 15 ÷ 5 = 3, 25 ÷ 5 = 5, and 5 ÷ 5 = 1. Hence the simplest ratio is 3:5:1. Option A is the original ratio and is not simplified. Option B is correct because all three terms were divided by the same common factor and the result has no common factor greater than 1. Option C, 1:5:3, changes the first and third positions and does not match the data. Option D, 1:2:3, also gives different relative values. The fact that the gases are at the same temperature and pressure allows their volumes to be compared directly, but it does not require a special gas-law calculation here. Exam reminder: preserve order and divide every term equally.

Multiple proportions apply to different compounds of the same two elements. Exam tip: look for same two elements.

Multiple proportions apply to different compounds of the same two elements. Exam tip: look for same two elements.

Multiple proportions apply to different compounds of the same two elements. Exam tip: look for same two elements.

Multiple proportions apply to different compounds of the same two elements. Exam tip: look for same two elements.

Multiple proportions apply to different compounds of the same two elements. Exam tip: look for same two elements.

The governing concept is the law of definite proportions, also called the law of constant composition. It states that a particular pure compound always contains the same elements combined in a fixed ratio by mass, regardless of the source or quantity of the sample. Every sample of CaCl₂ therefore contains calcium and chlorine in the same mass relationship. The statement does not describe conservation of mass, which concerns total mass before and after a reaction. It also does not compare two different compounds, as required by the law of multiple proportions, and it is unrelated to gaseous volume ratios. Hence option D is correct.

The governing principle is the law of definite proportions, or constant composition. A pure compound has a fixed chemical formula, so the elements in it occur in a constant ratio by mass in every sample. K₂O always contains potassium and oxygen in the same mass relationship; changing the sample size changes the total amounts but not their percentages. The conservation law refers to the unchanged total mass in a chemical process. The multiple-proportions law compares the masses of one element that combine with a fixed mass of another in two or more different compounds, not repeated samples of one compound. The gaseous-volumes law concerns reacting gases. Therefore option A is correct.

The key concept is the law of definite proportions, which states that a pure compound always contains the same constituent elements in a fixed ratio by mass. Since all the samples named here are pure AlCl₃, each contains aluminium and chlorine in the same mass percentages, even if the samples differ in size or origin. The law of conservation of mass describes the total mass balance during a reaction, not the composition of a compound. The law of multiple proportions requires comparison of different compounds made from the same elements. The law of gaseous volumes deals with volume relationships among reacting gases. Thus the wording about different samples of one pure compound leads directly to option B.

The governing idea is constant composition. The law of definite proportions says that every pure sample of a given compound contains its constituent elements in an unchanging mass ratio. Methane, CH₄, therefore has the same carbon and hydrogen percentages in every pure sample, although the total mass of the samples may differ. This is not the conservation of mass, because no reaction or before-and-after mass comparison is described. It is not multiple proportions, because that law compares different compounds formed by the same elements. It is also not the law of gaseous volumes, which concerns volume ratios of reacting gases under suitable conditions. Hence option C correctly names the law.

The law being tested is the law of definite proportions, also known as the law of constant composition. A pure compound has a definite formula and therefore contains its constituent elements in a fixed mass ratio. Consequently, every pure sample of Na₂O has the same relative amounts of sodium and oxygen by mass, even when the samples have different total masses. Conservation of mass would require a chemical reaction and a comparison of total mass before and after it. Multiple proportions concerns two or more different compounds made from the same elements. Gaseous volumes concerns volume relationships in gas reactions. Since the stem emphasizes different samples of one pure compound and identical percentages, option D is the only suitable answer.

Direct answer: Option A, in a closed system the total mass of reactants equals the total mass of products. Conservation of mass means that matter is neither created nor destroyed during a chemical reaction. Atoms only rearrange, so the total mass before and after reaction remains equal when nothing can enter or leave. Step by step: add the masses of all reactants; add the masses of all products; the two totals are equal. Option A is correct because it uses total mass and states the important closed-system condition. Option B is wrong because a mixture can have variable composition; its components need not be in a fixed ratio. Option C is wrong because gases have mass, even though they may be less dense and sometimes seem weightless. Option D is wrong because one particular product does not have to equal one particular reactant; conservation applies to the total mass, not to matching individual substances. Exam cue: write ‘total mass before = total mass after.’

The direct answer is B: the element ratio in a pure compound remains fixed. The law of definite proportions states that a particular pure compound always contains the same elements in the same fixed proportion by mass, regardless of where the sample comes from or how it was prepared. For example, pure water always contains hydrogen and oxygen in a fixed mass ratio. The important words are “pure compound” and “fixed composition.” Option A is wrong because a mixture does not have one fixed chemical composition; its components can be present in different amounts. Also, the total amount of a mixture can change. Option B is correct because it states the exact principle of definite proportions. Option C is wrong because gas volumes are not always equal; gas volume depends on conditions such as temperature, pressure and amount. Option D is wrong because chemical reactions do not make mass double in every case; mass is conserved in a closed system. Do not confuse a compound with a mixture: salt water can have changing amounts of salt and water, but pure sodium chloride has a fixed composition. The law concerns ratios of elements, not the size of the sample. Memory cue: definite proportions means “same compound, same element ratio,” not “same amount of mixture.”

In a closed vessel, no matter enters or leaves, so the total mass of reactants equals the total mass of products. Option B refers to multiple proportions. Exam tip: look for the phrase ‘closed system’.

Gay-Lussac's law is related to gas volume ratios. Exam tip: remember same temperature and pressure.

Reciprocal proportions are related to mass comparison of three elements. Exam tip: look for the third element clue.