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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
After working out those calculations, we found that the number of molecules in the ideal gas is approximately \(9.44 \times 10^{23}\).

Step by step solution

01

Convert given values to proper units

To use the ideal gas equation, we need to convert all of the given values to proper units. Here, the temperature is given in Kelvin, which is the correct unit. However, the pressure is given in kilopascal (kPa) so we need to convert it to Pascal (Pa), as 1 kPa = 1000 Pa. So, the pressure \(P = 180,000 \, Pa\). The volume \(V = 8.5 \, L\) is already in the correct unit.
02

Use the ideal gas law to find the number of moles

By re-arranging the ideal gas law equation \(PV = nRT\) to solve for \(n\) (the number of moles), we have \(n = PV/RT\). Substituting the given values and the gas constant (\(R = 8.31 J/mol\cdot K\)), we find the number of moles \(n = \frac{180000 \cdot 8.5}{8.31 \cdot 350}\).
03

Use Avogadro's number to find the number of molecules

Using Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol), we can find the number of molecules by multiplying the number of moles found in step 2 above by Avogadro's number. Hence, the number of molecules = \(n \times Avogadro's \, number\).

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Most popular questions from this chapter

Prove the equation \(\beta=3 \alpha\) (Section 17.3 ) by considering a cube of side \(s\) and therefore volume \(V=s^{3}\) that undergoes a small temperature change \(d T\) and corresponding length and volume changes \(d s\) and \(d V\).

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The atmospheres of relatively low-mass planets like Earth don't contain much hydrogen (H \(_{2}\) ), while more massive planets like Jupiter have considerable atmospheric hydrogen. What factors might account for the difference?

How is it possible to have boiling water at a temperature other than \(100^{\circ} \mathrm{C} ?\)

Show that the coefficient of volume expansion of an ideal gas at constant pressure is the reciprocal of its kelvin temperature.
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