Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 29

What mass of ice can be melted with the same quantity of heat as required to raise the temperature of \(3.50 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}(1)\) by \(50.0^{\circ} \mathrm{C} ?\left[\Delta H_{\text {fusion }}^{\circ}=6.01 \mathrm{kJ} / \mathrm{mol}\right.\) \(\left.\mathrm{H}_{2} \mathrm{O}(\mathrm{s})\right]\)

Short Answer

Expert verified
The number of moles of ice that could be melted using the same amount of heat required to raise the temperature of \(3.50 \mathrm{mol}\) water by \(50.0^{\circ} \mathrm{C}\) can be calculated using the heat of fusion and standard specific heat principles. Then, convert that result from moles to grams using the molar mass of water

Step by step solution

01

Calculate the heat required to raise the temperature of water

Firstly, let's find out how much heat is needed to raise the temperature of liquid water by \(50.0^{\circ} \mathrm{C}\). This can be calculated using the formula Q=mcΔT. Where Q represents heat energy, m is the number of moles, c refers to the specific heat capacity of water (4.18 kJ/mol•K), and ΔT is the change in temperature (50°C in this case). Thus, Q needed for water: \(Q = 3.50 \mathrm{mol} * 4.18 \mathrm{kJ/mol•K} * 50 \mathrm{K}\)
02

Calculate the heat required to melt ice

Next, let's calculate how much heat is needed to change the state of water from solid (ice) to liquid using the same heat found in step 1. This can be done using the formula Q=ΔHfusion*n, where ΔHfusion is the heat of fusion of water (6.01 kJ/mol) and n is the number of moles. Thus, to find out the mass of ice that can be melted, we need to rearrange the formula to n = Q / ΔHfusion, and plug in the values.
03

Adjust for grams

Lastly, remember that to convert the number of moles to grams, we need to multiply number of moles by the molar mass of water (18 g/mol). Thus, the mass of ice that could be melt is: Mass = n * molar mass of water

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Construct a concept map to show the interrelationships between path-dependent and pathindependent quantities in thermodynamics.

Acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) torches are used in welding. How much heat (in kJ) evolves when 5.0 L of \(C_{2} \mathrm{H}_{2}\) \(\left(d=1.0967 \mathrm{kg} / \mathrm{m}^{3}\right)\) is mixed with a stoichiometric amount of oxygen gas? The combustion reaction is $$\begin{array}{r} \mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})+\frac{5}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \\ \Delta H^{\circ}=-1299.5 \mathrm{kJ} \end{array}$$

A handbook lists two different values for the heat of combustion of hydrogen: \(33.88 \mathrm{kcal} / \mathrm{g} \mathrm{H}_{2}\) if \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) is formed, and \(28.67 \mathrm{kcal} / \mathrm{g} \mathrm{H}_{2}\) if \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) is formed. Explain why these two values are different, and indicate what property this difference represents. Devise a means of verifying your conclusions.

Hot water and a piece of cold metal come into contact in an isolated container. When the final temperature of the metal and water are identical, is the total energy change in this process (a) zero; (b) negative; (c) positive; (d) not enough information.

Several factors are involved in determining the cooking times required for foods in a microwave oven. One of these factors is specific heat. Determine the approximate time required to warm \(250 \mathrm{mL}\) of chicken broth from \(4^{\circ} \mathrm{C}\) (a typical refrigerator temperature) to \(50^{\circ} \mathrm{C}\) in a \(700 \mathrm{W}\) microwave oven. Assume that the density of chicken broth is about \(1 \mathrm{g} / \mathrm{mL}\) and that its specific heat is approximately \(4.2 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1}\).
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Inorganic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Analysis

Read Explanation

The Earths Atmosphere

Read Explanation
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.

Sign-up for free