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Chapter 14: Problem 11

It takes \(0.16 \mathrm{g}\) of helium (He) to fill a balloon. How many grams of nitrogen \(\left(\mathrm{N}_{2}\right)\) would be required to fill the balloon to the same pressure, volume, and temperature?

Short Answer

Expert verified
1.12 grams of nitrogen are required.

Step by step solution

01

Introduction to Molar Mass

Before we solve the problem, let's understand the molar masses. Helium has an atomic mass of approximately 4 g/mol, and \(_2\) nitrogen has a molecular mass of approximately 28 g/mol.
02

Determine Moles of Helium

First, calculate the number of moles of helium using its mass and molar mass. The formula is \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\). Thus, for helium, \(0.16 \, \text{g} = \frac{0.16}{4} \, \text{mol}\).
03

Calculate Moles of Nitrogen

Since the conditions of pressure, volume, and temperature are the same, the number of moles of helium is equal to the number of moles of nitrogen required. Therefore, \(\text{moles of } \mathrm{N}_{2} = \frac{0.16}{4} \, \text{mol}\).
04

Convert Moles to Grams

Now convert the moles of nitrogen back to grams using the molar mass of nitrogen \( (28 \, \text{g/mol}) \). Calculate: \(\text{grams of } \mathrm{N}_{2} = \left(\frac{0.16}{4}\right) \times 28 \).
05

Final Calculation

By computing the above, \(\text{grams of } \mathrm{N}_{2} = 0.04 \, \text{mol} \times 28 \, \text{g/mol} = 1.12 \, \text{g}\). This is the mass of nitrogen needed.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Helium
Helium is a noble gas with the chemical symbol He. It is the second lightest and second most abundant element in the observable universe. Being a noble gas, helium is colorless, tasteless, and inert, meaning it does not easily form compounds with other elements.
Helium is notable for its very low atomic mass of approximately 4 g/mol, making it significantly lighter than air. This property allows helium-filled balloons to float. It has a lower density compared to many other gases, such as nitrogen.
  • Helium's low atomic mass is crucial when calculating the number of moles in a certain mass of helium.
  • It is often used in applications where low density and inertness are beneficial, such as in balloons and as a protective gas in certain industrial processes.
Nitrogen
Nitrogen is a diatomic molecule, represented by the chemical formula \(_2\). It makes up approximately 78% of the Earth's atmosphere. Unlike helium, nitrogen is a reactive non-metal under specific conditions.
Nitrogen has a molar mass of about 28 g/mol, which is much higher than that of helium. This is key in comparing the two gases in scenarios involving equal conditions of pressure, volume, and temperature, such as in the balloon example.
  • The higher molar mass of nitrogen means that, when converting moles to grams, it will weigh more than the same number of moles of helium.
  • Nitrogen is used in a wide array of applications, from fertilizers to the production of ammonia.
Moles calculation
The concept of moles is central in chemistry for counting and conversions. A 'mole' is a quantity representing \(6.022 \times 10^{23}\) particles of a substance. This is known as Avogadro's number.
To find the number of moles (\

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Most popular questions from this chapter

The dimensions of a room are \(2.5 \mathrm{m} \times 4.0 \mathrm{m} \times 5.0 \mathrm{m} .\) Assume that the air in the room is composed of \(79 \%\) nitrogen \(\left(\mathrm{N}_{2}\right)\) and \(21 \%\) oxygen \(\left(\mathrm{O}_{2}\right) .\) At a temperature of \(22^{\circ} \mathrm{C}\) and a pressure of \(1.01 \times 10^{5} \mathrm{Pa}\) what is the mass (in grams) of the air?

The volume of an ideal gas is held constant. Determine the ratio \(P_{2} / P_{1}\) of the final pressure to the initial pressure when the temperature of the gas rises (a) from 35.0 to \(70.0 \mathrm{K}\) and \((\mathrm{b})\) from 35.0 to \(70.0^{\circ} \mathrm{C}\)

Air is primarily a mixture of nitrogen \(\mathrm{N}_{2}\) (molecular mass \(=\) \(28.0 \mathrm{u}\) ) and oxygen \(\mathrm{O}_{2}\) (molecular mass \(=32.0 \mathrm{u}\) ). Assume that each behaves like an ideal gas and determine the rms speed of the nitrogen and oxygen molecules when the air temperature is \(293 \mathrm{K}\).

The pressure of sulfur dioxide \(\left(\mathrm{SO}_{2}\right)\) is \(2.12 \times 10^{4} \mathrm{Pa} .\) There are 421 moles of this gas in a volume of \(50.0 \mathrm{m}^{3} .\) Find the translational rms speed of the sulfur dioxide molecules.

The diffusion constant for the amino acid glycine in water has a value of \(1.06 \times 10^{-9} \mathrm{m}^{2} / \mathrm{s} .\) In a \(2.0-\mathrm{cm}\) -long tube with a cross-sectional area of \(1.5 \times 10^{-4} \mathrm{m}^{2},\) the mass rate of diffusion is \(m / t=4.2 \times 10^{-14} \mathrm{kg} / \mathrm{s}\) because the glycine concentration is maintained at a value of \(8.3 \times 10^{-3} \mathrm{kg} / \mathrm{m}^{3}\) at one end of the tube and at a lower value at the other end. What is the lower concentration?
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