Question

Two elements \(X\) (at mass 16\()\) and \(Y\) (at mass 14\()\) combine to form compounds \(A, B\) and \(C .\) The ratio of different masses of Y which combine with a fixed mass of \(X\) in \(A, B\) and \(C\) is \(1: 3: 5 .\) lf 32 parts by mass of \(X\) combines with 84 parts by mass of \(Y\) and \(B\), then in \(C\). 16 parts by mass of \(\mathrm{X}\) will combine with (1) 14 parts by mass of \(\mathrm{Y}\) (2) 42 parts by mass of \(\mathrm{Y}\) (3) 70 parts by mass of \(\mathrm{Y}\) (4) 84 parts by mass of \(\mathrm{Y}\)

Short answer

In compound C, 16 parts by mass of X will combine with 70 parts by mass of Y.

Step-by-step solution

- Calculate the mass ratio in compound B

Given that 32 parts of mass of X combine with 84 parts by mass of Y in compound B. This gives the mass ratio of X to Y in compound B as \(\frac{84}{32} = 2.625:1\).

- Determine the relative masses for A, B, and C

The problem states the ratio of different masses of Y which combine with a fixed mass of X in A, B, and C is 1:3:5. Therefore, we use the proportion 1:3:5 to find the ratios.

- Calculate the mass of Y in compound C

If we let the mass of Y in compound A with a fixed mass of X be \(m\). For compound B, the mass of Y would then be \(3m\). Using the ratio, for compound C, the mass of Y would be \(5m\). Given \(3m = 84\), we have \(m = 28\). Therefore, in compound C, the mass of Y would be \(5m = 5 \times 28 = 140\).

- Compute the mass of Y that combines with 16 parts of X in C

The mass ratio of X to Y in compound B is \(\frac{84}{32} = 2.625\). The same fixed ratio holds for X and Y in C. So, if 32 parts of X combine with 140 parts of Y, then 16 parts of X will combine with \( \frac{140}{32} \times 16 = 70\).

Key concepts

Mass Ratio and Its Importance

Understanding mass ratio is crucial in stoichiometry. It tells us how much of one substance combines with a specific amount of another substance. In the given exercise, the ratio of masses of element Y combining with a fixed mass of element X in compounds A, B, and C is stated as 1:3:5. This ratio helps us identify how the masses of different elements interact in a chemical compound. When we say mass ratio, we mean the comparative weights of these substances.Imagine we have a fixed mass of X. The ratios 1:3:5 mean that if one part of X combines with 1 part of Y in compound A, in compound B, the same amount of X will combine with 3 parts of Y, and in compound C, it will combine with 5 parts of Y. This gives us a clear picture of the mass relationships as we solve the problem.Knowing these ratios allows chemists to predict the proportions of elements needed to form specific compounds, ensuring accurate chemical reactions.

Chemical Compounds and Their Formation

Chemical compounds are formed when two or more elements combine in definite proportions. When elements X and Y combine to form compounds A, B, and C, they do so following strict mass ratios. This showcases the Law of Definite Proportions, which states that a chemical compound always contains exactly the same proportion of elements by mass.In this context, compounds A, B, and C are formed with different amounts of element Y, but the mass of element X remains constant. This means we are observing how the mass of Y changes while keeping the mass of X fixed. Knowing the exact proportions helps in determining the correct amount of each element needed for the reaction. Understanding how these proportions shift allows us to predict the properties and composition of the resulting compound.This principle is vital in chemical engineering and various industrial processes where precise measurements and consistent product quality are crucial.

Fixed Mass: Solving the Exercise

The concept of a fixed mass is integral to solving the exercise. It simplifies calculations and allows for comparing different scenarios effectively. Here, the mass of X is kept constant while we study how different amounts of Y combine with it.To solve the problem, we start with the given data: 32 parts of X combine with 84 parts of Y in compound B. From this, we deduce the mass ratio, which is 84:32 or 2.625:1. Given the mass ratios 1:3:5 for A, B, and C, we know that mass of Y for B (84 parts) corresponds to 3 parts, making each part (m) 28 parts (since 3m=84).From here, we calculate the mass of Y for compounds A and C using these multiples. For compound C (which uses 5 parts of Y), the calculation is 5m = 5 x 28 = 140 parts of Y. If we then adjust these 140 parts for a different fixed mass of X (16 instead of 32), we use the same ratio: \(\frac{140}{32} \times 16=70\). The final answer tells us that 16 parts of X will combine with 70 parts of Y in compound C.This approach demonstrates why understanding and applying fixed mass ratios is essential for solving stoichiometric problems correctly.