The two common isotopes of chlorine with mass numbers 35 and 37 exist in approximately what ratio in nature?

Introduction / Context:
This general chemistry question focuses on isotopes of chlorine and their natural abundance. Understanding isotope ratios is important when calculating average atomic masses and when interpreting data from mass spectrometry and nuclear chemistry.

Given Data / Assumptions:

• Chlorine has two main stable isotopes with mass numbers 35 and 37.
• The question asks for their approximate natural abundance ratio.
• We consider the common textbook approximation used for basic chemistry calculations.
• The options are different simple integer ratios such as 1 : 2, 2 : 3, 3 : 1, 3 : 4 and 1 : 1.

Concept / Approach:
The atomic mass of chlorine listed in the periodic table is about 35.5 atomic mass units. This value is a weighted average of the masses of its isotopes based on their relative abundances. Since the average is much closer to 35 than to 37, the isotope with mass 35 must be more abundant. By considering a simple ratio that gives an average near 35.5, we can deduce the approximate ratio Cl 35 : Cl 37 as about 3 : 1, which corresponds closely to the known natural abundance values (roughly 75 percent for Cl 35 and 25 percent for Cl 37).

Step-by-Step Solution:
1) Let the ratio of Cl 35 to Cl 37 be a : b.2) The average atomic mass can be approximated as (35a + 37b) / (a + b).3) We want this to be around 35.5, the accepted average atomic mass of chlorine.4) If we try a simple ratio 3 : 1, the average becomes (35 * 3 + 37 * 1) / 4 = (105 + 37) / 4 = 142 / 4 = 35.5.5) Therefore, the approximate natural abundance ratio of the isotopes Cl 35 : Cl 37 is 3 : 1.

Verification / Alternative check:
From more detailed data, the abundance of Cl 35 is about 75.8 percent and that of Cl 37 is about 24.2 percent. If we divide 75.8 by 24.2, we get a value a little above 3, which again supports an approximate ratio of 3 : 1. This confirms that the commonly used textbook approximation is correct for basic multiple choice questions and average mass calculations.

Why Other Options Are Wrong:
1 : 2: This would give an average mass much closer to 36.3, which does not match the periodic table value of about 35.5.
2 : 3: This ratio also favours the heavier isotope too much and would not yield an average close to 35.5.
3 : 4: Here the heavy isotope fraction is still too large, shifting the average atomic mass away from the accepted chlorine value.
1 : 1: Equal amounts of Cl 35 and Cl 37 would give an average of 36, which again disagrees with the actual atomic weight of chlorine.

Common Pitfalls:
Students sometimes guess that isotopes must be present in equal proportions, which is rarely true in nature. Another common error is to memorise a wrong ratio or to ignore the link between the ratio and the average atomic mass. Always check whether a proposed ratio gives an average mass consistent with the value printed in the periodic table, as this is an easy way to verify your choice in such questions.

Final Answer:
The isotopes chlorine 35 and chlorine 37 exist in nature in the approximate ratio 3 : 1.