Answer to Question #149611 in General Chemistry for bianca

Question

1. A sample of fluorine gas has a density of
g/L at a pressure of 1.21 atm and a temperature of 47 °C. Assume ideal behavior.

2. A sample of hydrogen gas has a density of
g/L at a pressure of 0.913 atm and a temperature of 36 °C. Assume ideal behavior.

3. The average molecular speed in a sample of gas at a certain temperature is 397 m/s.
The average molecular speed in a sample of gas is
m/s at the same temperature.

Answer 1

1. Density is mass per unit volume. Since we're assuming ideal behavior, we can rearrange the ideal gas law to yield density.

PV = nRT

Since we know the identity of the gas, we can easily convert from n (moles of gas) to mass of gas. n will need to be in our numerator. Volume needs to be in the denominator. We can divide by V and RT from both sides:

PV / (VRT) = nRT / (VRT) = P / (RT) = n / V

Now we convert moles to mass using molar mass (g substance / mole substance):

n (GMM) / V = m / V = P * GMM / (RT)

Let's apply this:

molar mass of fluorine gas: 2 * atomic mass fluorine atom = 38.00 g / mol

density: m / V = (1.21 atm) (38.00 g F₂ / mol F₂) / [(0.08206 L * atm / K * mol) (47 + 273 K)] = 1.75 g / L

2. Mr(H₂) = 1 x 2 = 2.0 g / mol

density = m / V = (0.913 atm) (2.0 g H₂ / mol H₂) / [(0.08206 L * atm / K * mol) (36 + 273 K)] = 0.072 g / L

3. Average speed of molecule is given as:

v = (8RT/πM)^1/2

v_CO2 / v_H2 = (M_H2 / M_CO2)^1/2

397 m/s / v_H2 = (2 g/mol / 44 g/mol)^1/2 = 1 / (22)^1/2

v_H2 = 397 m/s x (22)^1/2 = 1862 m/s