/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 64 A 2.30-g sample of white solid w... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

A 2.30-g sample of white solid was vaporized in a 345\(\mathrm{mL}\) vessel. If the vapor has a pressure of \(985 \mathrm{mmHg}\) at \(148^{\circ} \mathrm{C}\), what is the molecular weight of the solid?

Short Answer

Expert verified
The molecular weight of the solid is approximately 169 g/mol.

Step by step solution

01

Convert Pressure to Atmospheres

The pressure of the gas is given in mmHg. We need to convert it to atmospheres for our calculations. There are 760 mmHg in one atmosphere.\[\text{Pressure in atm} = \frac{985 \text{ mmHg}}{760 \text{ mmHg/atm}} \approx 1.296 \text{ atm}\]
02

Convert Temperature to Kelvin

The given temperature is in degrees Celsius. To use the ideal gas law, we need to convert it to Kelvin.\[T(\text{K}) = T(\text{°C}) + 273.15 = 148 + 273.15 = 421.15 \text{ K}\]
03

Convert Volume to Liters

The volume of the vessel is given in milliliters. To use it in our calculations, we convert it to liters. There are 1000 mL in 1 L.\[V(\text{L}) = \frac{345 \text{ mL}}{1000 \text{ mL/L}} = 0.345 \text{ L}\]
04

Use the Ideal Gas Law to Find Moles

The ideal gas law equation is \(PV = nRT\). We need to solve for \(n\), the number of moles.\[PV = nRT \rightarrow n = \frac{PV}{RT}\]Using \(R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}\), we calculate:\[n = \frac{(1.296 \text{ atm})(0.345 \text{ L})}{(0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1})(421.15 \text{ K})} \approx 0.0136 \text{ mol}\]
05

Calculate Molecular Weight

With the moles of the gas determined, use the mass of the sample to calculate molecular weight, which is mass per mole.\[\text{Molecular Weight} = \frac{\text{Mass}}{\text{Moles}} = \frac{2.30 \text{ g}}{0.0136 \text{ mol}} \approx 169 \text{ g/mol}\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Molecular Weight
Molecular weight is an important concept in chemistry that tells us the mass of a single molecule of a substance. It is expressed as grams per mole (g/mol). To find molecular weight, we divide the mass of the sample by the number of moles. For example, when you know a sample weighs 2.30 grams and contains 0.0136 moles, calculating the molecular weight is straightforward.
Using the formula \( \text{Molecular Weight} = \frac{\text{Mass}}{\text{Moles}} \), you simply divide the mass by the number of moles. This helps us understand how much one mole of the solid would weigh.
In practical terms, knowing the molecular weight allows chemists to measure out exact quantities of substances for reactions.
Pressure Conversion
Pressure conversion is necessary when dealing with different units that measure pressure. In this problem, we start with mmHg (millimeters of mercury) and need to convert to atmospheres (atm). One atmosphere is defined as 760 mmHg.
To convert mmHg to atm, use the formula:
  • \( \text{Pressure in atm} = \frac{\text{Pressure in mmHg}}{760} \)
So for a pressure of 985 mmHg, the conversion results in approximately 1.296 atm.
This conversion is crucial because the ideal gas law often uses atmosphere as the standard unit for pressure. Accurate conversion ensures the correct application of the gas laws.
Temperature Conversion
Temperature in gas calculations must often be in Kelvin, a unit that begins at absolute zero. The Kelvin scale is necessary because it ensures that temperatures are always positive, avoiding negative values that can disrupt calculations.
To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature:
  • \( T(\text{K}) = T(\text{°C}) + 273.15 \)
For example, 148°C becomes 421.15 K.
Using Kelvin in the ideal gas law \( PV = nRT \), the temperature variable must be in this unit so that the gas constant \( R \) used in calculations matches with pressure in atmospheres and volume in liters.
Volume Conversion
Volume conversion is an essential step when working with gases and the ideal gas law. Here, the volume is given in milliliters, but needs to be converted to liters because the gas constant \( R \) in the ideal gas law uses liters.
The conversion is simple:
  • 1 liter = 1000 milliliters
Given a volume like 345 mL, convert it to liters by dividing by 1000:
  • \( V(\text{L}) = \frac{345 \text{ mL}}{1000} = 0.345 \text{ L} \)
Using liters in calculations ensures consistency with the units of pressure and temperature, allowing for accurate application of the ideal gas law.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For a spacecraft or a molecule to leave the moon, it must reach the escape velocity (speed) of the moon, which is \(2.37 \mathrm{~km} / \mathrm{s}\). The average daytime temperature of the moon's surface is \(365 \mathrm{~K}\). What is the rms speed (in \(\mathrm{m} / \mathrm{s}\) ) of a hydrogen molecule at this temperature? How does this compare with the escape velocity?

Lithium hydroxide, LiOH, is used in spacecraft to recondition the air by absorbing the carbon dioxide exhaled by astronauts. The reaction is $$2 \mathrm{LiOH}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{Li}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l)$$ What volume of carbon dioxide gas at \(21^{\circ} \mathrm{C}\) and \(781 \mathrm{mmHg}\) could be absorbed by \(327 \mathrm{~g}\) of lithium hydroxide?

Formic acid, \(\mathrm{HCHO}_{2}\), is a convenient source of small quantities of carbon monoxide. When warmed with sulfuric acid, formic acid decomposes to give \(\mathrm{CO}\) gas. $$\mathrm{HCHO}_{2}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}(g)$$ If \(3.85 \mathrm{~L}\) of carbon monoxide was collected over water at \(25^{\circ} \mathrm{C}\) and \(689 \mathrm{mmHg}\), how many grams of formic acid were consumed?

If \(0.10 \mathrm{~mol}\) of \(\mathrm{I}_{2}\) vapor can effuse from an opening in a heated vessel in \(39 \mathrm{~s}\), how long will it take \(0.10 \mathrm{~mol} \mathrm{H}_{2}\) to effuse under the same conditions?

If \(456 \mathrm{dm}^{3}\) of krypton at \(101 \mathrm{kPa}\) and \(21^{\circ} \mathrm{C}\) is com- pressed into a \(27.0-\mathrm{dm}^{3}\) tank at the same temperature, what is the pressure of krypton in the tank?

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.