The molecular mass of oxygen molecules is 32, and the molecular mass of nitrogen molecules is 28. If these two gases are at the same temperature, the ratio of nitrogen's r m s speed to that of oxygen is:
(8)1/2:(7)1/2
8:7
(7)1/2:(8)1/2
7:8
13
To find the ratio of nitrogen's RMS speed to that of oxygen, we can use the equation:
Ratio = √( M1 / M2 )
Where M1 is the molecular mass of oxygen and M2 is the molecular mass of nitrogen.
Given that the molecular mass of oxygen is 32 and the molecular mass of nitrogen is 28, we can substitute these values into the equation:
Ratio = √( 32 / 28 )
Now we can simplify the equation:
Ratio = √( 8 / 7 )
To further simplify this, we take the square root of both the numerator and denominator:
Ratio = √8 / √7
Since both numerator and denominator share the same square root, we can rewrite the ratio as:
Ratio = (√8 / √7) * (√7 / √7)
Multiplying the terms together, we get:
Ratio = (√(8 * 7)) / (√(7 * 7))
Simplifying further:
Ratio = (√56) / (√49)
Finally, we can evaluate the square root of 56 and 49:
Ratio = 7√2 / 7
Simplifying the expression, the ratio of nitrogen's RMS speed to that of oxygen is:
Ratio = √2 : 1
Therefore, the correct answer is (8)1/2 : 1.