Question

use the references to access important values if needed for this question.
arrange the following elements and/or compounds in order of increasing average molecular speed. all are at the same temperature.
ammonia, argon, sulfur dioxide, neon
1 (slowest) 2 3 4 (fastest)
____ < __ < __ < ____
drag and drop your selection from the following list to complete the answer:
ne nh₃ so₂ ar

Explanation:

Step1: Recall the formula for average molecular speed

The formula for the average molecular speed (\(v_{avg}\)) is \(v_{avg}=\sqrt{\frac{8RT}{\pi M}}\), where \(R\) is the gas constant, \(T\) is the temperature, and \(M\) is the molar mass of the gas. At the same temperature (\(T\) is constant), the average molecular speed is inversely proportional to the square - root of the molar mass (\(v_{avg}\propto\frac{1}{\sqrt{M}}\)). So, the larger the molar mass (\(M\)), the slower the average molecular speed.

Step2: Calculate the molar masses

• The molar mass of \(SO_{2}\): \(M_{SO_{2}}=(32.07 + 2\times16.00)\space g/mol=64.07\space g/mol\)
• The molar mass of \(Ar\): \(M_{Ar}=39.95\space g/mol\)
• The molar mass of \(Ne\): \(M_{Ne}=20.18\space g/mol\)
• The molar mass of \(NH_{3}\): \(M_{NH_{3}}=(14.01+3\times1.01)\space g/mol = 17.04\space g/mol\)

Step3: Compare the molar masses

Since \(M_{SO_{2}}>M_{Ar}>M_{Ne}>M_{NH_{3}}\), using the relationship \(v_{avg}\propto\frac{1}{\sqrt{M}}\), the order of increasing average molecular speed (from slowest to fastest) is based on the reverse order of molar masses.

Answer:

\(SO_{2}