(I) At room temperature, an oxygen molecule, with mass of 5.31 x 10⁻²⁶ kg, typically has a kinetic energy of about 6.21 x 10⁻²¹ J . How fast is it moving?

Verified step by step guidance

1. Identify the given values: mass of the oxygen molecule (m) = 5.31 x 10⁻²⁶ kg, kinetic energy (KE) = 6.21 x 10⁻²¹ J.
2. Recall the formula for kinetic energy: KE = $\frac{1}{2}m{v}^2$, where m is mass and v is velocity.
3. Rearrange the formula to solve for velocity (v): $v=\sqrt{\frac{2\times KE}{m}}$.
4. Substitute the given values into the rearranged formula: $v=\sqrt{\frac{2\times 6.21\times 10⁻²¹}{5.31\times 10⁻²⁶}}$.
5. Calculate the square root to find the velocity of the oxygen molecule.

Key Concepts

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In this context, the kinetic energy of the oxygen molecule is given, which allows us to determine its speed by rearranging the formula to solve for v.

Mass

Mass is a measure of the amount of matter in an object, typically expressed in kilograms. In this question, the mass of the oxygen molecule is provided as 5.31 x 10⁻²⁶ kg, which is essential for calculating its velocity using the kinetic energy formula.

Velocity

Velocity is a vector quantity that describes the speed of an object in a specific direction. In this scenario, we need to calculate the velocity of the oxygen molecule based on its kinetic energy and mass, which will provide insight into its motion at room temperature.