Imagine that you dissolve 10.0 g of a mixture of NaNO3 and KF in 100.0 g of water and find that the temperature rises by 2.22 °C. Using the following data, calculate the mass of each compound in the original mixture. Assume that the specific heat of the solution is 4.18 J>1 g °C2 NaNO31s2 S NaNO31aq2 ΔH = + 20.4 kJ>mol KF1s2 S KF1aq2 ΔH = - 17.7 kJ>mol

Verified step by step guidance

Determine the total heat absorbed or released by the solution using the formula: \( q = m \times c \times \Delta T \), where \( m \) is the mass of the solution, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

Convert the total heat calculated in step 1 from joules to kilojoules since the enthalpy changes for the dissolution processes are given in kJ/mol.

Let \( x \) be the mass of NaNO3 and \( y \) be the mass of KF. Write the equation based on the conservation of mass: \( x + y = 10.0 \, g \).

Use the enthalpy changes for each compound to set up an equation for the heat of the solution: \( \frac{x}{molar \, mass \, of \, NaNO3} \times 20.4 + \frac{y}{molar \, mass \, of \, KF} \times (-17.7) = total \, heat \, in \, kJ \) from step 2.

Solve the system of equations from steps 3 and 4 to find the values of \( x \) and \( y \), which represent the masses of NaNO3 and KF in the mixture, respectively.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Thermochemistry

Thermochemistry is the study of the heat energy associated with chemical reactions and physical transformations. In this context, it involves understanding how the dissolution of NaNO3 and KF in water affects the temperature of the solution, which is indicative of the heat absorbed or released during the process. The temperature change can be used to calculate the enthalpy changes associated with the dissolution of these compounds.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. In this problem, the specific heat of the solution (4.18 J/g°C) is crucial for calculating the total heat absorbed by the water when the temperature rises. This value allows us to relate the temperature change to the heat involved in the dissolution of the salts.

Molar Enthalpy of Solution

Molar enthalpy of solution refers to the heat change that occurs when one mole of a solute dissolves in a solvent. The given values for NaNO3 (+20.4 kJ/mol) and KF (-17.7 kJ/mol) indicate whether the dissolution process is endothermic or exothermic. These values are essential for determining the contributions of each compound to the overall temperature change and for calculating the mass of each compound in the original mixture.

Recommended video:

Guided course

02:34

Enthalpy of Formation

Related Practice

Textbook Question

We said in Section 9.1 that the potential energy of water at the top of a dam or waterfall is converted into heat when the water dashes against rocks at the bottom. The potential energy of the water at the top is equal to EP = mgh, where m is the mass of the water, g is the acceleration of the falling water due to gravity 1g = 9.81 m>s22, and h is the height of the water. Assuming that all the energy is converted to heat, calculate the temperature rise of the water in degrees Celsius after falling over California's Yosemite Falls, a distance of 739 m. The specific heat of water is 4.18 J/(g·K).

Textbook Question

When a gaseous compound X containing only C, H, and Ois burned in O2, 1 volume of the unknown gas reacts with3 volumes of O2 to give 2 volumes of CO2 and 3 volumesof gaseous H2O. Assume all volumes are measured at thesame temperature and pressure.(d) Combustion of 5.000 g of X releases 144.2 kJ heat.Look up ΔH°f values for CO21g2 and H2O1g2 inAppendix B, and calculate ΔH°f for compound X.

Textbook Question

Given 400.0 g of hot tea at 80.0 °C, what mass of ice at 0 °C must be added to obtain iced tea at 10.0 °C? The specific heat of the tea is 4.18 J>1g °C2 and ΔHfusion for ice is + 6.01 kJ>mol.

Textbook Question

9.149 Consider the reaction: 4 CO1g2 2 NO21g2 4 CO21g2 N21g2. Using the following information, determine ΔH° for the reaction at 25 °C. NO1g2 ΔH°f = + 91.3 kJ>mol CO21g2 ΔH°f = - 393.5 kJ>mol 2 NO1g2 + O21g2 S 2 NO21g2 ΔH° = - 116.2 kJ 2 CO1g2 + O21g2 S 2 CO21g2 ΔH° = - 566.0 kJ

views

Textbook Question

Combustion analysis of 0.1500 g of methyl tert-butyl ether, an octane booster used in gasoline, gave 0.3744 g of CO2 and 0.1838 g of H2O. When a flask having a volume of 1.00 L was evacuated and then filled with methyl tertbutyl ether vapor at a pressure of 100.0 kPa and a temperature of 54.8 °C, the mass of the flask increased by 3.233 g. (d) The enthalpy of combustion for methyl tert-butyl ether is ΔH° combustion = -3368.7 kJ>mol. What is its standard enthalpy of enthalpy of formation, ΔH°f?

Textbook Question

Phosgene, COCl₂(g), is a toxic gas used as an agent of warfare in World War I. (b) Using the table of bond dissociation energies (Table 9.3) and the value ΔH°f = 716.7 kJ/mol for C(g), estimate ΔH°_f for COCl₂(g) at 25 °C. Compare your answer to the actual ΔH°_f given in Appendix B, and explain why your calculation is only an estimate.