Question

physical science the average velocity v of gas molecules is represented by the formula $v = sqrt{\frac{3kt}{m}}$. the velocity is measured in meters per second, t is the temperature in kelvin, and m is the molar mass of the gas in kilograms per mole. the variable k represents a value called the molar gas constant, which is about 8.3. write a simplified radical expression that represents the average velocity of gas molecules that have a temperature of 300 kelvin and a mass of 0.045 kilogram per mole. round to the nearest meter per second. m/s

Explanation:

Step1: Substitute values into formula

Given $k = 8.3$, $t=300$, $m = 0.045$, substitute into $V=\sqrt{\frac{3kt}{m}}$, we get $V=\sqrt{\frac{3\times8.3\times300}{0.045}}$.

Step2: Calculate numerator

First calculate $3\times8.3\times300 = 3\times2490=7470$. So $V=\sqrt{\frac{7470}{0.045}}$.

Step3: Calculate fraction value

$\frac{7470}{0.045}= \frac{7470}{\frac{45}{1000}}=7470\times\frac{1000}{45}=\frac{7470000}{45}=166000$. So $V = \sqrt{166000}$.

Step4: Simplify square - root

$\sqrt{166000}=\sqrt{10000\times16.6}=100\sqrt{16.6}$.

Step5: Approximate value

$\sqrt{16.6}\approx 4.0743$, then $100\sqrt{16.6}\approx100\times4.0743 = 407.43\approx407$.

Answer:

$407$