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Chapter 11: Problem 6

Suppose that \(3.00 \mathrm{~g}\) of gaseous nitrogen, \(\mathrm{N}_{2}\), is placed in a \(2.00 \mathrm{~L}\) container. The pressure is measured to be \(450.5 \mathrm{~mm} \mathrm{Hg}\). What is the Celsius temperature of the gas? (Hint: Your first step should be solving the ideal gas equation for \(T\).)

Short Answer

Expert verified
The Celsius temperature of the gas is approximately \(60.74 \degree C\).

Step by step solution

01

Solve the Ideal Gas Law equation for T

To find the temperature of the gas, we need to solve the Ideal Gas Law equation for T: PV = nRT Divide both sides of the equation by nR to isolate T: T = PV / nR
02

Convert pressure from mm Hg to atm

The Ideal Gas Law requires pressure to be in atm, but we are given the pressure in mm Hg. We need to convert the pressure to atm using the conversion factor: 1 atm = 760 mm Hg. Pressure(in atm) = Pressure(in mm Hg) * (1 atm / 760 mm Hg) Pressure = 450.5 * (1 / 760) Pressure ≈ 0.593 atm
03

Convert the mass of N₂ to moles

We are given the mass of nitrogen (N₂) in grams, but the Ideal Gas Law requires the number of moles. First, we need to determine the molar mass of N₂ (28.02 g/mol) by adding the atomic mass of two nitrogen atoms (14.01 g/mol each). Then, we can convert the mass to moles using the molar mass of nitrogen. Number of moles (n) = mass / molar mass Number of moles = 3.00 g / 28.02 g/mol Number of moles ≈ 0.107 mol
04

Substitute the values into the equation and solve for T in Kelvin

Now we can substitute the given values into the equation and solve for the temperature in Kelvin. T = PV / nR T = (0.593 atm)(2.00 L) / (0.107 mol)(0.0821 L·atm/mol·K) T ≈ 333.89 K
05

Convert temperature from Kelvin to Celsius

Finally, we need to convert the temperature from Kelvin to Celsius using the formula: Celsius Temperature = Kelvin Temperature - 273.15 Celsius Temperature = 333.89 K – 273.15 Celsius Temperature ≈ 60.74 °C So, the Celsius temperature of the gas is approximately 60.74 °C.

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Most popular questions from this chapter

Are gases denser or less dense than liquids and solids? Explain.

An automobile tire at \(22^{\circ} \mathrm{C}\) with an internal volume of \(20.0 \mathrm{~L}\) is filled with air to a total pressure of 30 psi (pounds per square inch). \(\left[1 \mathrm{~atm}=14.696 \mathrm{lb} / \mathrm{in} .^{2}\right]\) (a) What is the amount in moles of air in the tire? (b) If the air were entirely nitrogen \(\left(\mathrm{N}_{2}\right)\), how many grams of it would be in the tire? How many pounds of it would be in the tire? \([453.6 \mathrm{~g}=1 \mathrm{lb}]\)

Under what two conditions are gas molecules unable to overcome the weak attractive forces that exist between them?

True or false? \(1 \mathrm{~atm}=76 \mathrm{~mm} \mathrm{Hg}=760 \mathrm{~cm} \mathrm{Hg}\). If false, fix it.

If we continuously compress a real gas in a cylinder with a movable piston while keeping the container at a constant temperature in an ice bath: (a) What will eventually happen to the gas and why? (b) How well will the ideal gas law apply to the real gas shown when it is close to doing what you said it will do in part (a)?
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