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Chapter 5: Problem 25

Which noble gas has the smallest density at STP? Explain.

Short Answer

Expert verified
Helium (He) has the smallest density at STP with a value of 0.1786 g/L. This is due to its low molar mass of 4 g/mol compared to other noble gases, resulting in fewer mass units per unit volume.

Step by step solution

01

List the Noble Gases

The noble gases are a group of chemical elements in the 18th column of the periodic table. They are as follows: Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Xe), and Radon (Rn).
02

Find Molar Masses of the Noble Gases

Look up the molar masses of each noble gas from the periodic table: - Helium (He): 4 g/mol - Neon (Ne): 20 g/mol - Argon (Ar): 40 g/mol - Krypton (Kr): 84 g/mol - Xenon (Xe): 131 g/mol - Radon (Rn): 222 g/mol
03

Understand the Ideal Gas Law and Density Equation

We can use the Ideal Gas Law equation to find the density of each noble gas under STP conditions. The Ideal Gas Law equation is as follows: \(PV = nRT\) Where P is pressure, V is volume, n is the amount of gas in moles, R is the ideal gas constant, and T is the temperature. Under STP conditions, the pressure is 1 atm, and the temperature is 273.15 K (0掳C). Since we're looking for the density (\(\rho\)), we must rearrange the equation: \(\rho = \frac{m}{V} = \frac{nM}{V}\) Where m is the mass of the gas, M is the molar mass, and V is its volume. Replacing n by combining the Ideal Gas Law equation and applying STP conditions, we have: \(\rho = \frac{MP}{RT}\)
04

Calculate the Density of Each Noble Gas at STP

Using the density equation above and the molar masses from Step 2, calculate the density for each noble gas at STP: - Helium (He): \(\rho = \frac{(4 g/mol)(1 atm)}{(0.0821 L/mol \cdot K)(273.15 K)} = 0.1786\, g/L\) - Neon (Ne): \(\rho = \frac{(20 g/mol)(1 atm)}{(0.0821 L/mol \cdot K)(273.15 K)} = 0.8995\, g/L\) - Argon (Ar): \(\rho = \frac{(40 g/mol)(1 atm)}{(0.0821 L/mol \cdot K)(273.15 K)} = 1.7990\, g/L\) - Krypton (Kr): \(\rho = \frac{(84 g/mol)(1 atm)}{(0.0821 L/mol \cdot K)(273.15 K)} = 3.6753\, g/L\) - Xenon (Xe): \(\rho = \frac{(131 g/mol)(1 atm)}{(0.0821 L/mol \cdot K)(273.15 K)} = 5.7695\, g/L\) - Radon (Rn): \(\rho = \frac{(222 g/mol)(1 atm)}{(0.0821 L/mol \cdot K)(273.15 K)} = 9.9196\, g/L\)
05

Comparing and Explaining the Smallest Density

As per the density values calculated above, Helium (He) has the smallest density at STP with a value of 0.1786 g/L. Helium has the smallest density because it has the lowest molar mass among all noble gases, which results in fewer mass units per unit volume. This is due to the atomic configuration of helium, which contains only two electrons and two protons. The low molar mass and the properties of the ideal gas law equation ensure that helium has the lowest density among noble gases at STP.

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