A certain automobile tire has a volume of 0.0185 m³.If the absolute (or total)pressure in the tire is 500 kPa and the temperature is 298 K,how many molecules are there inside the tire? (R = 8.31 J/mol ∙ K,N_A = 6.022 × 10²³ molecules/mol) A)2.25 × 10²³ molecules B)2.25 × 10²⁴ molecules C)3.25 × 10²³ molecules D)3.25 × 10²⁴ molecules E)3.25 × 10²⁵ molecules

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Quizplus · Accepted Answer

To find the number of molecules, we can use the ideal gas law in the form $PV = nRT$, where $P$ is the pressure, $V$ is the volume, $n$ is the number of moles, $R$ is the ideal gas constant, and $T$ is the temperature. Rearranging for $n$, we get $n = \frac{PV}{RT}$. Given $P = 500 \times 10^3$ Pa (since 1 kPa = 1000 Pa), $V = 0.0185$ m^3, $R = 8.31$ J/mol·K, and $T = 298$ K, we can calculate $n$. Then, to find the number of molecules, we multiply $n$ by Avogadro's number ($6.022 \times 10^{23}$ molecules/mol).$n = \frac{PV}{RT} = \frac{(500 \times 10^3) \times 0.0185}{8.31 \times 298}$Calculating $n$ gives us the number of moles, which we then multiply by Avogadro's number to get the total number of molecules. The calculation will show that the number of molecules is closer to $2.25 \times 10^{24}$, making option B the correct answer.

A Certain Automobile Tire Has a Volume of 0