What is the average speed of a molecule F¬2 at 300 C?

chemsolution x

What is the average speed of a molecule F­2 at 300 C?

 

An unknown mass gas has the formula ClxOy and has a density of 2.875 g/L at 756 mmHg and 11 C. What is the most likely molecular formula of the gas?

 

Answers are in the attached file with detailed explanations

3. What is the average speed of a molecule F2 at 300 C?

The average velocity of gas particles is found using the root mean square velocity formula
μrms = (3RT/M) ½
where
μrms = root mean square velocity in m/sec
R = ideal gas constant = 8.3145 (kg·m2/sec2)/K·mol
T = absolute temperature in Kelvin
M = mass of a mole of the gas in kilograms.

Solution:

Convert temperature to Kelvin (K):

T = 300 +273

T = 573 K

Find molar mass:

Mass of F = 18. 998 g/mol

Since it is diatomic and there are two Flourine molecules,

Molar mass = 2 (18. 998 g/mol)

= 38 g/mol or 38×10-3 kg/mol

Find μrms

μrms = (3RT/M) ½
μrms = [3(8.3145 (kg·m2/sec2)/K·mol) (573 K)/38 x 10-3 kg/mol]½
μrms = 613.288 m/seconds (Answer)

4. An unknown mass gas has the formula ClxOy and has a density of 2.875 g/L at 756 mmHg and 11 C. What is the most likely molecular formula of the gas?

Solution:

Recall the ideal gas law equation:

PV = nRT

where P = pressure in atm

V = volume in liter

R = 0.0821 liter·atm/mol·K 

n = number of moles

T = temperature in Kelvin

n = m/MW

where m = mass

MW = molecular weight

so,

PV = m/MW * RT

MW = (m/V) *RT/P

but we know that density (d) = m/V so

MW = d*RT/P

yet we need to convert T in Kelvin and pressure in atm

T = 11 + 273

T = 284 K

P = 756 mmHg (1 atm/ 760 mmHg)

P = 0.995 atm

Substitute these values with R and d to the equation MW = d*RT/P

MW = (2.875 g/L)( 0.0821 L·atm/mol·K )( 284 K)/( 0.995 atm)

MW = 67.372 g/mol

Now recall that,

The molar mass of Cl = 35.45 g/mol and O = 16 g/mol

The total mass of ClxOy = MW = 67.372 g/mol, so the equation out of the masses is

35.45x + 16y = 67.372

We can only do trial and error here since we cannot set-up another equation. But we remember that we can only take integer values for x and y

If we assume x = 2 for example 2(35.45) = 70.9. Oops! This value already exceeds 67.372.

Definitely we can’t make x=0 as it would mean nonexistence of Cl.

If we assume x = 1 35.45<67.372

So x=1 is good.

Now we manipulate 35.45x + 16y = 67.372 and express in terms of y

y = [67.372- 35.45(1)]/16

y = 1.995 (we can round it to 2)

y = 2

Now as a summary we have x=1 and y=2

so ClxOy = Cl1O2 or ClO2

The molecular formula is likely ClO2. (Answer)