Question 6 What is the number ofmo ecules in 500cm^3 understandard conditions? A 6.02times 10^23times 0.5 B. 6.02times 10^23times 500 C (22.7)/(0.5)times 6.02times 10^23 D (0.5)/(22.7)times 6.02times 10^23

To determine the number of molecules in 500 cm³ under standard conditions, we need to use the ideal gas law and Avogadro's number.<br /><br />First, let's recall that under standard conditions (0°C and 1 atm), 1 mole of an ideal gas occupies 22.7 liters (or 22700 cm³).<br /><br />Given:<br />- Volume = 500 cm³<br />- 1 mole of gas occupies 22700 cm³<br /><br />We can set up a proportion to find the number of moles:<br /><br />\[<br />\frac{500 \text{ cm}^3}{22700 \text{ cm}^3} = \frac{x \text{ moles}}{1 \text{ mole}}<br />\]<br /><br />Solving for \( x \):<br /><br />\[<br />x = \frac{500}{22700} \text{ moles}<br />\]<br /><br />Next, we multiply the number of moles by Avogadro's number (\(6.02 \times 10^{23}\) molecules/mole) to find the number of molecules:<br /><br />\[<br />\text{Number of molecules} = \left( \frac{500}{22700} \right) \times 6.02 \times 10^{23}<br />\]<br /><br />Simplifying this expression:<br /><br />\[<br />\text{Number of molecules} = \frac{500}{22700} \times 6.02 \times 10^{23}<br />\]<br /><br />This matches option D:<br /><br />\[<br />\text{D } \frac{0.5}{22.7} \times 6.02 \times 10^{23}<br />\]<br /><br />Therefore, the correct answer is:<br /><br />D. \(\frac{0.5}{22.7} \times 6.02 \times 10^{23}\)