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Determine the root-mean-square sped of CO2 molecules that have an average Kinetic Energy of 4.21x10^-21 J per molecule. Write your answer to 3 sig figs.

E = 1/2 m v^2 

If you substitute into this formula, you will get out the root-mean-square speed. 

If energy is Joules, the mass should be in kg, and the speed will be in m/s. 

1 mol of CO2 is 44.0 g, or 4.40 x 10^1 g or 4.40 x 10^-2 kg. 

If you divide this by Avagadro's constant, you will get the average mass of a CO2 molecule. 

4.40 x 10^-2 kg / 6.02 x 10^23 = 7.31 x 10^-26 kg 

So, if E = 1/2 mv^2 

v^2 = 2E/m = 2 (4.21x10^-21 J)/7.31 x 10^-26 kg = 115184.68 
Take the square root of that, and you get the answer 339 m/s.
onyebuchinnaji

The root-mean square speed of the CO₂ molecules is 339 m/s.

The given parameters;

  • average kinetic energy of CO₂ = 4.2 x 10⁻²¹ J per molecule

The molecular mass of the CO₂ = (12 + 16x2) = 44 g = 0.044 kg

The average mass of the CO₂ molecule is calculated as;

[tex]average \ mass \ = \frac{molecular \ mass}{Avogadro's \ number} = \frac{0.044}{6.02 \times 10^{23}} = 7.31 \times 10^{-26} \ kg[/tex]

The root-mean square speed is calculated by applying kinetic energy equation;

[tex]E = \frac{1}{2} mv^2\\\\v^2 = \frac{2E}{m} \\\\v= \sqrt{\frac{2E}{m}} \\\\v = \sqrt{\frac{2(4.2 \times 10^{-21})}{7.31\times 10^{-26}}}\\\\v = 338.99 \ m/s \ \approx 339 \ m/s[/tex]

Thus, the root-mean square speed is 339 m/s.

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