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Chapter 2: Problem 44

Two elements, R and Q, combine to form two binary compounds. In the first compound, 14.0 g of R combines with 3.00 g of Q. In the second compound, 7.00 g of R combines with 4.50 g of Q. Show that these data are in accord with the law of multiple proportions. If the formula of the second compound is RQ, what is the formula of the first compound?

Short Answer

Expert verified
The mass ratios of R to Q for the two compounds are \(\frac{14}{3}\) and \(\frac{7}{9}\). Comparing these ratios results in a whole number ratio of \(6:1\), which confirms that the data is consistent with the law of multiple proportions. Since the second compound's formula is RQ, and the first compound has 6 times more Q than the second while having the same amount of R, the formula of the first compound is \(R Q_6\) or R6Q.

Step by step solution

01

Calculate the Mass Ratios

We are given: 1st compound: 14.0 g of R combines with 3.00 g of Q 2nd compound: 7.00 g of R combines with 4.50 g of Q Let's calculate the mass ratios by dividing the mass of R by the mass of Q for each compound: 1st compound ratio: \( \frac{14.0}{3.00} \) 2nd compound ratio: \( \frac{7.00}{4.50} \)
02

Simplify the Mass Ratios and Find the Whole Number Ratio

Simplify the fractions to get the simplest form of the mass ratios (divide both the numerator and denominator of the fractions by their greatest common divisor): 1st compound simplified ratio: \( \frac{14.0}{3.0} = \frac{14}{3} \) 2nd compound simplified ratio: \( \frac{7.0}{4.5} = \frac{7}{9} \) Now, compare the mass ratios to find a whole number ratio: Whole number ratio: \( \frac{\frac{14}{3}}{\frac{7}{9}} = \frac{14}{3} \cdot \frac{9}{7} \)
03

Calculate the Whole Number Ratio and Verify the Law of Multiple Proportions

Multiply the fractions and simplify to get the whole number ratio: Whole number ratio: \( \frac{14}{3} \cdot \frac{9}{7} = \frac{14 \cdot 9}{3 \cdot 7} = \frac{2 \cdot 3}{1} = 6 \) Since we obtained a whole number ratio (6:1), this data is in accord with the law of multiple proportions.
04

Determine the Formula of the First Compound

We know that the second compound is RQ. From the whole number ratio we found, the amount of Q in the first compound is 6 times larger than in the second compound, while the amount of R remains the same. So, the formula of the first compound will include R and 6 times more Q than the second compound, resulting in the formula being \( R Q_6 \) or R6Q.

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