Question

Calculate the root-mean-square velocity, in m/s, for an oxygen

molecule at 35.0 °C. The universal gas constant, R=8.314 J/mol･K.
Report to three significant figures.

Answer 1

To find the root-mean-square velocity of an oxygen molecule at 35.0 °C, use the formula Urms = √(3RT/M) with the temperature converted to Kelvin and the molar mass in kg/mol. The calculated rms velocity is approximately 1554 m/s.

Step-by-step explanation:

To calculate the root-mean-square (rms) velocity for an oxygen molecule at a given temperature, the following formula can be used:

Urms = √(3RT/M)

Where:

• Urms is the root-mean-square velocity
• R is the universal gas constant (8.314 J/mol·K)
• T is the temperature in Kelvin
• M is the molar mass of oxygen in kg/mol (32.0 g/mol = 0.032 kg/mol since 1 g = 0.001 kg)

First, we need to convert the temperature from degrees Celsius to Kelvin:

T(K) = 35.0 °C + 273.15 = 308.15 K

Now we can calculate the rms velocity:

Urms = √(3 * 8.314 J/mol·K * 308.15 K / 0.032 kg/mol) = √(3 * 8.314 * 308.15 / 0.032)

Urms = √(77308.627 / 0.032)

Urms = √(2415890.84375)

Urms = 1554.309 m/s

The root-mean-square velocity of an oxygen molecule at 35.0 °C is therefore approximately 1554 m/s, when rounded to three significant figures.

Answer 2

The root-mean-square velocity of an oxygen molecule at 35.0 °C is approximately 15.55 m/s.

Step-by-step explanation:

The root-mean-square velocity of an oxygen molecule at 35.0 °C can be calculated using the formula:

Urms = √(3RT/M)

where R is the universal gas constant (8.314 J/mol･K), T is the temperature in Kelvin, and M is the molar mass of oxygen (32.0 g/mol).

Converting 35.0 °C to Kelvin (temperature in K) gives 308.15 K.

Substituting the values into the formula:

Urms = √(3 * 8.314 * 308.15 / 32.0)

Urms = √(7741.158075 / 32.0)

Urms = √241.9105641

Urms ≈ 15.55 m/s