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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°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°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

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.

At what Kelvin temperature will \(25.2 \mathrm{~mol}\) of Xe occupy a volume of \(645 \mathrm{~L}\) at a pressure of 732 torr?

If \(250 \mathrm{~mL}\) of \(\mathrm{O}_{2}\) measured at STP, are obtained by the decomposition of the \(\mathrm{KClO}_{3}\) in a \(1.20\)-g mixture of \(\mathrm{KCl}\) and \(\mathrm{KClO}_{3}\), $$ 2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g) $$ what is the percent by mass of \(\mathrm{KClO}_{3}\) in the mixture?

A sample of \(\mathrm{CH}_{4}\) gas was collected over water at \(29^{\circ} \mathrm{C}\) and 749 \(\mathrm{mm} \mathrm{Hg}\). What is the partial pressure of the \(\mathrm{CH}_{4}\) ? (Refer to Appendix 5 for the vapor pressure of water.)

Perform the following pressure in conversions: (a) Convert 649 torr to \(\mathrm{kPa}\). (b) Convert \(5.07 \mathrm{kPa}\) to atm. (c) Convert \(3.64 \mathrm{~atm}\) to \(\mathrm{mm} \mathrm{Hg}\). (d) Convert 803 torr to atm. (e) Convert \(1.08 \mathrm{~atm}\) to \(\mathrm{cm} \mathrm{Hg}\).
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