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Chapter 12: Problem 53

How many moles of air are in 1.00 \(\mathrm{L}\) at \(-23^{\circ} \mathrm{C}\) and 101 \(\mathrm{kPa}\) ?

Short Answer

Expert verified
The number of moles of air are approximately 0.048 moles.

Step by step solution

01

Convert temperature to Kelvin

We have the temperature given as -23°C. Since all gas law equations require the temperature to be in Kelvin, we must add 273.15 to this value to convert it from Celsius to Kelvin. Thus, the temperature \(T = -23 + 273.15 = 250.15 K\).
02

Convert pressure to atm

The pressure is given as 101 kPa. The Ideal Gas Law is generally used with pressure in atm, so we must convert the pressure from kPa to atm. The conversion factor is 1 atm = 101.325 kPa. So,\( P = \frac{101}{101.325} = 0.9968 atm \).
03

Use the Ideal Gas Law

The Ideal Gas Law is \(PV = nRT\), where \(P\) is the pressure in atm, \(V\) is the volume in liters, \(n\) is the number of moles, \(R\) is the gas constant (0.08206 atm.L/mol.K), and \(T\) is the temperature in Kelvin. To solve for \(n\), rearrange the equation as \(n = \frac{PV}{RT}\). Substitute the given values into the equation to find the number of moles: \(n = \frac{(0.9968 atm)(1.00 L)}{(0.08206 atm.L/mol.K)(250.15 K)}\).
04

Calculate the number of moles

After substituting the known values into the equation, simplify to get the number of moles. This will give us the answer.

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