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Chapter 12: Problem 37

What volume would result if a balloon were filled with \(10.0\) grams of chlorine gas at STP?

Short Answer

Expert verified
The volume of the balloon would be 3.2 liters.

Step by step solution

01

- Determine the Molar Mass of Chlorine Gas

Chlorine gas (Cl\textsubscript{2}) has a molar mass of 35.5 grams per mole for each chlorine atom. Since chlorine gas is diatomic, multiply this value by 2:\(M_{Cl_2} = 35.5 \text{ g/mol} \times 2 = 70 \text{ g/mol}\)
02

- Convert Grams to Moles

Use the molar mass to convert the given mass of chlorine gas to moles. The formula is:\(n = \frac{mass}{molar\text{ }mass}\)For our case:\(n = \frac{10.0 \text{ g}}{70 \text{ g/mol}} = 0.143 \text{ mol}\)
03

- Use the Ideal Gas Law at STP

At Standard Temperature and Pressure (STP), one mole of any ideal gas occupies 22.4 liters. Multiply the number of moles by this volume:\(V = n \times 22.4 \text{ L/mol}\)For our case:\(V = 0.143 \text{ mol} \times 22.4 \text{ L/mol} = 3.2 \text{ L}\)

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Key Concepts

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

ideal gas law
The Ideal Gas Law is a fundamental equation in chemistry that describes the behavior of gases. The equation is expressed as: \(PV = nRT\) where:
  • P = Pressure of the gas
  • V = Volume of the gas
  • n = Number of moles of the gas
  • R = Universal gas constant (0.0821 L·atm/mol·K)
  • T = Temperature in Kelvin
The Ideal Gas Law assumes that the gas behaves ideally, meaning there are no interactions between gas molecules, and the volume of the gas molecules themselves is negligible. This law is very useful for predicting how changes in pressure, volume, temperature, or amount of gas will affect the other variables.
molar mass
Molar mass is the mass of one mole of a given substance, usually expressed in grams per mole (g/mol). It directly relates to the molecular weight of the substance. For example, chlorine gas (Cl2) is diatomic, meaning it consists of two chlorine atoms in each molecule. Each chlorine atom has a molar mass of 35.5 g/mol. Therefore, the molar mass of chlorine gas is: \(M_{Cl_2} = 35.5 \text{ g/mol} \times 2 = 70 \text{ g/mol}\) Understanding molar mass is crucial for converting between grams and moles, which is a common task in chemistry problems involving gases.
STP conditions
STP stands for Standard Temperature and Pressure. These conditions are used as a reference point for expressing gas volumes and behaviors. At STP, the temperature is 273.15 K (0°C), and the pressure is 1 atmosphere (atm). Under these conditions, one mole of any ideal gas occupies a volume of 22.4 liters. These standard conditions simplify calculations because it provides a consistent reference:
  • Temperature = 273.15 K (0°C)
  • Pressure = 1 atm
  • Volume of 1 mole of gas = 22.4 L
Using STP conditions, you can easily calculate the volume of gas if the number of moles is known. This is extremely helpful for solving problems involving gas laws.
volume calculation
When calculating the volume of a gas, knowing the number of moles and the conditions under which the gas is measured (e.g., STP) is essential. Using the Ideal Gas Law, and specifically under STP, we can simplify the formula to find volume. Given that at STP, one mole of gas occupies 22.4 liters, you can calculate the volume of a gas using:\(V = n \times 22.4 \text{ L/mol}\) For example, if you have 0.143 moles of chlorine gas at STP, the volume is computed as:\(V = 0.143 \text{ mol} \times 22.4 \text{ L/mol} = 3.2 \text{ L}\) This formula simplifies the volume calculation for any ideal gas under STP conditions.

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Most popular questions from this chapter

Consider the following equation: $$ 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ (a) How many liters of oxygen are required to react with \(2.5 \mathrm{~L}\) \(\mathrm{NH}_{3}\) ? Both gases are at STP. (b) How many grams of water vapor can be produced from \(25 \mathrm{~L}\) \(\mathrm{NH}_{3}\) if both gases are at STP? (c) How many liters of NO can be produced when \(25 \mathrm{~L}\) \(\mathrm{O}_{2}\) are reacted with \(25 \mathrm{~L} \mathrm{} \mathrm{NH}_{3}\) ? All gases are at the same temperature and pressure.

The internal pressure on a bottle of soda is 5570 torr. The bottle cap is designed to withstand a pressure of \(7.0 \mathrm{~atm}\). (a) Calculate the pressure in atm. (b) Calculate the pressure in psi. (c) Calculate the pressure in \(\mathrm{kPa}\). (d) Is the bottle cap at risk of failing?

At what Kelvin temperature will \(37.5 \mathrm{~mol}\) of Ar occupy a volume of \(725 \mathrm{~L}\) at a pressure of 675 torr?

Using the ideal gas law, \(P V=n R T\), calculate the following: (a) the volume of \(0.510 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) at \(47^{\circ} \mathrm{C}\) and \(1.6\) atm pressure (b) the number of grams in \(16.0 \mathrm{~L}\) of \(\mathrm{CH}_{4}\) at \(27^{\circ} \mathrm{C}\) and 600 . torr pressure (c) the density of \(\mathrm{CO}_{2}\) at \(4.00\) atm pressure and \(20.0^{\circ} \mathrm{C}\) (d) the molar mass of a gas having a density of \(2.58 \mathrm{~g} / \mathrm{L}\) at \(27^{\circ} \mathrm{C}\) and \(1.00\) atm pressure.

A steel cylinder contains \(50.0 \mathrm{~L}\) of oxygen gas under a pressure of \(40.0 \mathrm{~atm}\) and at a temperature of \(25^{\circ} \mathrm{C}\). What was the pressure in the cylinder during a storeroom fire that caused the temperature to rise \(152^{\circ} \mathrm{C}\) ? (Be careful!)
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