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Chapter 17: Problem 18

How many molecules are in an ideal-gas sample at \(350 \mathrm{K}\) that occupies \(8.5 \mathrm{L}\) when the pressure is \(180 \mathrm{kPa} ?\)

Short Answer

Expert verified
The number of molecules in the ideal-gas sample approximately amounts to \(3.73 \times 10^{22}\)

Step by step solution

01

Identify the given values

The given values are: \n Pressure \(P = 180 \times 10^3 \, \text{Pa}\),\n Volume \(V = 8.5 \, \text{L} = 8.5 \times 10^{-3} \, \text{m}^3\), \n Temperature \(T = 350 \, \text{K}\). \n We also know that the Gas constant \(R = 8.314 \, \text{JK}^{-1}\text{mol}^{-1}\)
02

Apply the ideal gas law

Following the ideal gas law \(P \cdot V = n \cdot R \cdot T\), we can rearrange it to solve for n, the number of moles: \n \(n = \frac{P \cdot V}{R \cdot T}\)
03

Compute the number of moles

Substituting the values into the formula from step 2, we find \n \(n = \frac{(180\times10^3 \, \text{Pa})(8.5\times10^{-3}\, \text{m}^3)}{(8.314 \, \text{JK}^{-1}\text{mol}^{-1})(350 \, K)} \approx 0.062 \, \text{mol}\)
04

Use Avogadro's Number to find the number of molecules

We know from Avogadro's number that 1 mole has \(6.02214076 \times 10^{23}\) molecules. So to find the number of molecules, we multiply the number of moles by Avogadro's number: \n Number of molecules = \(n \times (\text{Avogadro's number}) \approx 0.062 \times 6.02214076 \times 10^{23}\)

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Most popular questions from this chapter

The average speed of the molecules in a gas increases with increasing temperature. What about the average velocity?

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