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bdog123 bdog123
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8 months ago
At 200 K, the molecules or atoms of an unknown gas, X, have an average velocity equal to that of Ar atoms at 400 K. What is X? (Assume ideal behavior.)


He

CO

HF

HBr

F2
Textbook 

Chemistry: An Atoms First Approach


Edition: 3rd
Authors:
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Tiffani372Tiffani372
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8 months ago Edited: 2 weeks ago, bio_man
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Answer:

Step 1: Explanation

The average speed is given by the following equation:

speed = √ (3RT)/M =   (3RT/M)1/2 where, M = molar mass and T = Temperature and R = gas constant

Step 2: Extract the data

Given

(Speed)argon =  √ (3R × 400 K ) /40 g/mol [ note: molar mass of argon = 40 g/mol ]

(Speed)unknown =  √ (3R × 200 K ) /M 

Step 3: Calculation

Here, (Speed)argon = (Speed)unknown

√ (3R × 400 K ) /40 g/mol =    √ (3R × 200 K ) /M 

Here, 3R as well as under root sign also gets cancelled out

=> 400 K /40 g/mol = 200 K /M

=>   2 /40 g/mol = 1 /M

=>  M = ( 40 g/mol / 2) = 20 g/mol ----option(c) HF

Given, (a) He = molar mass =4 g/mol

(b) He = molar mass =4 g/mol

(c) HF = molar mass = 20 g/mol matched with the calculated answer

(d) HBr = molar mass = 81 g/mol

(e) F2 = molar mass = 38g/mol

Hence, the answer is HF
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