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Chapter 12: Problem 34

How many grams of \(\mathrm{C}_{3} \mathrm{H}_{6}\) are present in \(945 \mathrm{~mL}\) of the gas at STP?

Short Answer

Expert verified
Approximately 1.78 grams of \(\text{C}_3\text{H}_6\) are present in 945 mL of the gas at STP.

Step by step solution

01

- Understand STP conditions

Standard Temperature and Pressure (STP) is defined as a temperature of 273.15 K (0掳C) and a pressure of 1 atm. Under these conditions, one mole of any gas occupies 22.4 liters.
02

- Convert the volume to liters

Given volume is 945 mL. Convert milliliters to liters by dividing by 1000: 945 mL = 0.945 L
03

- Use the molar volume at STP

At STP, 1 mole of any gas occupies 22.4 liters. Set up a proportion to find the number of moles of \(\text{C}_{3}\text{H}_{6}\): \[ \text{Number of moles} = \frac{0.945 \text{ L}}{22.4 \text{ L/mol}} \]
04

- Calculate the number of moles

Perform the division to find the number of moles: \[ \text{Number of moles} = \frac{0.945}{22.4} \approx 0.0422 \text{ moles} \]
05

- Determine the molar mass of \(\text{C}_{3}\text{H}_{6}\)

To find the molar mass, add the atomic masses of all atoms in the molecule: \text{C}: 12.01 g/mol \text{H}: 1.01 g/mol \[(3 \times 12.01) + (6 \times 1.01) = 36.03 + 6.06 = 42.09 \text{ g/mol} \]
06

- Calculate the mass of gas

Use the molar mass and the number of moles to find the mass: \[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \] \[ \text{Mass} = 0.0422 \text{ moles} \times 42.09 \text{ g/mol} \] \text{Mass} \approx 1.78 \text{ grams}

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Key Concepts

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

Standard Temperature and Pressure (STP)
Standard Temperature and Pressure, commonly called STP, refers to a set of conditions used to standardize measurements in chemistry. At STP, the temperature is set to 273.15 K (which equals 0掳C), and the pressure is set to 1 atmosphere (atm). Understanding STP is important because it allows scientists to accurately compare and predict the behavior of gases under these standard conditions.
Molar Volume of Gas
The molar volume of a gas at STP is a crucial concept in gas calculations. One mole of any ideal gas occupies 22.4 liters at STP. This relationship is derived from the Ideal Gas Law and provides a straightforward method to convert between the volume of a gas and the number of moles. For example, if you know the volume of a gas at STP, you can easily determine the amount in moles by dividing by 22.4 L/mol.
Molar Mass Calculation
Calculating the molar mass of a compound involves adding the atomic masses of all the atoms in the molecule. For instance, the molar mass of \(\text{C}_{3}\text{H}_{6}\) is 42.09 g/mol. This is calculated by adding the masses of three carbon atoms (each 12.01 g/mol) and six hydrogen atoms (each 1.01 g/mol). Accurately determining the molar mass is essential for converting between the number of moles and the mass of a substance in grams.
Stoichiometry
Stoichiometry is the field of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. It's a key concept when determining the amounts of substances involved in reactions. In our exercise, stoichiometry helps us understand the relationship between the volume of \(\text{C}_{3}\text{H}_{6}\) gas at STP, its molar volume, and ultimately its mass. Through stoichiometric calculations, we can move seamlessly from volume (945 mL) to moles (0.0422 moles) and then to mass (approximately 1.78 grams).

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Most popular questions from this chapter

Fish contain a collapsible swim bladder containing air that they use to help them maintain buoyancy so they can swim at any level and not sink or float. If a swordfish has a fish bladder with a volume of \(32.7 \mathrm{~L}\) at sea level where the pressure is 755 torr and the temperature is \(28^{\circ} \mathrm{C}\), what will the volume of the swim bladder be if the swordfish dives under the water to catch some mackerel where the pressure is 2577 torr and the temperature is \(12^{\circ} \mathrm{C}\) ?

This scuba diver watch shows the air pressure in the diver's scuba tank as \(1920 \mathrm{lb} /\) in. \({ }^{2}\). Convert this pressure to (a) atm (b) torr (c) \(\mathrm{kPa}\)

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Which of these has the greatest density? (a) \(\mathrm{SF}_{6}\) at \(\mathrm{STP}\) (b) \(\mathrm{C}_{2} \mathrm{H}_{6}\) at room conditions (c) \(\mathrm{He}\) at \(-80^{\circ} \mathrm{C}\) and \(2.15\) atm

You are responsible for ensuring that the giant American eagle balloon stays inflated at the local Veterans Day parade. You inflate the balloon to a pressure of 976 torr using \(5.27 \times 10^{5} \mathrm{~mol}\) of helium in the morning when the temperature is \(12^{\circ} \mathrm{C}\). At the end of the day the temperature increases to \(31^{\circ} \mathrm{C}\) and \(15.0 \%\) of the helium seeps out of the balloon. (a) How many moles of air will be left in the balloon at the end of the day after \(15.0 \%\) is lost? (b) What will the pressure of the balloon be at the end of the day if the volume is unchanged?
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