Question

Calculate the root mean square speed of fluorine gas at 425˚c. please answer in units of m/s.

Answer 1

The root mean square speed of fluorine gas at 425°C is 677 m/s.

FURTHER EXPLANATION

The root mean square speed of a gas is a measure of how fast gas particles move. It is affected by the molecular mass of the gas and the temperature.

To solve for the root mean square speed, $v_{rms}$ , the following equation is used:

$v_{rms} \ = \sqrt{\frac{3RT}{M} }$

where:

R = gas constant = $8.314 \ \frac{J}{mol - K} \ = 8.314 \ \frac{kg - m^2}{K-mol-s^2}$

T = temperature in Kelvin

M = molecular mass in $\frac{kg}{mol}$

To find the root mean square speed of fluorine gas, sort the given information first:

T = 425°C

M of fluorine gas, $F_2$ = 38 g/mol

Ensure that the quantities are expressed with the correct units. In this case, the temperature must first be converted to K as follows:

$T \ in \ K \ = ^oC \ + \ 273.15\\T \ in \ K \ = 425^oC \ + \ 273.15\\\boxed {T \ = 698.15 \ K}$

Next, the molecular mass of fluorine must be expressed in kg:

$molecular \ mass \ in \ kg \ = given \ mass \ in \frac{g}{mol} \ (\frac{1 \ kg}{1000 \ g})\\molecular \ mass \ of \ F_2 \ = 38 \frac{g}{mol} \ (\frac{1 \ kg}{100 \ g})\\\boxed {molecular \ mass \ of \ F_2 \ = 0.038 \frac{kg}{mol}}$

Now that all values are expressed in the correct units, they may be plugged into the equation for $v_{rms}$:

$v_{rms} \ = \sqrt{\frac{3RT}{M} }\\v_{rms} \ = \sqrt{\frac{3(8.314 \frac{kg-m^2}{K-mol-s^2})(698.15 \ K)}{0.038 \frac{kg}{mol}}$

$v_{rms} \ = \sqrt{458243.61 \frac{m^2}{s^2} }\\\boxed {v_{rms} \ = 676.93 \frac{m}{s}}$

Since the given in the problem has 3 significant figures only, then the final answer should be 677 m/s.

LEARN MORE

• Maxwell - Boltzmann Distribution brainly.com/question/900885
• Kinetic Molecular Theory brainly.com/question/2084651
• Ideal Gas Law brainly.com/question/12936013

Keywords: root mean square speed

Answer 2

 The root mean square speed of a gas is calculated through the equation,

       Vrms = sqrt (3RT/M)

where:
      Vrms = root mean square velocity/speed
      R = universal gas constant
      T = temperature
      M = molar mass of the gas

Fluorine gas is a diatomic particle, F2, with a molar mass equal to 37.997 g/mol. Substituting the known values to the equation,

      Vrms = sqrt (3)(0.0821 L.atm/mol.K)(425 + 273.15)) / 37.997 g/mol))
         Vrms = sqrt ((3)(0.0821 L atm)(101325 kg/ms²/1 atm))(698.15 K) (1 m³/1000L)/ (37.997 g)(1 kg/1000g))
       Vrms = 25.63 m/s

ANSWER: 25.63 m/s