A chemist places 1.750 g of ethanol, $\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O},$ in a bomb calorimeter with a heat capacity of 12.05 kJ/K. The sample is burned and the temperature of the calorimeter increases by $4.287^{\circ} \mathrm{C}$. Calculate $\Delta E$ for the combustion of ethanol in kJ/mol.

If $3.365 \mathrm{~g}$ of ethanol $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)$ is burned completely in a bomb calorimeter at $298.15 \mathrm{~K}$, the heat produced is $99.472 \mathrm{~kJ}$. a. Estimate $\Delta H_{\text {combustion }}^{\circ}$ for ethanol at $298.15 \mathrm{~K}$. b. Estimate $\Delta H_{f}^{\circ}$ of ethanol at $298.15 \mathrm{~K}$ .

Match each function in Column I with the appropriate description in Column II. $y = 3 sin(2x — 4)$, A. amplitude=2, period=$\frac{\pi}{2}$, phase shift=$\frac{3}{4}$, B. amplitude=3, period=$\pi$, phase shift=2, C. amplitude=4, period$=\frac{2 \pi}{3}$, phase shift=$\frac{2}{3}$, D. amplitude=2, period=$\frac{2 \pi}{3}$, phase shift=$\frac{4}{3}$.

A 21.8 g sample of ethanol C2H5OH is burned in a bomb calorimeter, according to the following reaction. If the temperature rises from 25.0 °C to 62.3°C, determine the heat capacity of the calorimeter. The molar mass of ethanol is 46.07 g/mol.

Write a balanced equation and draw an approximate enthalpy diagram for each of the following changes: (a) the combustion of 1 mol of liquid methanol (CH3OH); (b) the formation of 1 mol of nitrogen dioxide from its elements (heat is absorbed).

Use the elimination method to solve the systems.

$$\begin{aligned} x+2 y &=7 \\ 3 x+5 y &=19 \end{aligned}$$

A $30.5 \mathrm{~g}$ sample of an alloy at $93.0^{\circ} \mathrm{C}$ is placed into $50.0 \mathrm{~g}$ of water at $22.0^{\circ} \mathrm{C}$ in an insulated coffee cup with a heat capacity of $9.2 \mathrm{~J} / \mathrm{K}$. \

If the final temperature of the system is $31.1^{\circ} \mathrm{C}$, what is the specific heat capacity of the alloy?

A $30.5~\mathrm{g}$ sample of an alloy at $93.0 ^ { \circ } \mathrm { C }$ is placed into $50.0~\mathrm{g}$ of water at $22.0 ^ { \circ } \mathrm { C }$ in an insulated coffee cup with a heat capacity of $9.2 \mathrm{~J/K}$. If the final temperature of the system is $31.1 ^ { \circ } \mathrm { C },$ what is the specific heat capacity of the alloy?

Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence interval for the mean weight gain this supplement produces has a margin of error of

$$\pm 11$$

pounds. Some students wrote the following conclusions. Did anyone interpret the interval correctly? Explain any misinterpretations. We're 95% sure that a cow fed this supplement will gain between 45 and 67 pounds.

Perform the indicated operations. (-7.2a^2b^3 + 4.1ab^2 - 3.9b) - (0.8a^2b^3 - 3.2ab^2 - b)

Consider the following balanced thermochemical equation for the decomposition of the mineral magnesite: $\mathrm { MgCO } 3 ( \mathrm { s } ) \rightarrow \mathrm { MgO } ( \mathrm { s } ) + \mathrm { CO } 2 ( \mathrm { g } ) \Delta \mathrm { Hrxn } = 117.3 \mathrm { kJ }$

Is heat absorbed or released in the reaction?

A 27.7-g sample of ethylene glycol, a car radiator coolant, loses 688 J of heat. What was the initial temperature of the ethylene glycol if the final temperature is $32.5 ^ { \circ } \mathrm { C }$ (c of ethylene glycol = $2.42 J/g \cdot K$) ?

A 27.7-g sample of ethylene glycol, a car radiator coolant, loses $688 \mathrm{~J}$ of heat.
What was the initial temperature of the ethylene glycol if the final temperature is $32.5^{\circ} \mathrm{C}$ ( $c$ of ethylene glycol $=2.42 \mathrm{~J} / \mathrm{g} \cdot \mathrm{K})$ ?

Diamond and graphite are two crystalline forms of carbon. At 1 atm and $25 ^ { \circ } \mathrm { C }$ diamond changes to graphite so slowly that the enthalpy change of the process must be obtained indirectly. Determine $\triangle$ Hrxn for C(diamond) $\rightarrow$ C(graphite) with equations from the following list: (1) $C(dianond) + O _ { 2 } ( g ) \longrightarrow \mathrm { CO } _ { 2 } ( g ) \quad \Delta H = - 395.4 \mathrm { kJ }$ (2) $2 \mathrm { CO } _ { 2 } ( g ) \longrightarrow 2 \mathrm { CO } ( g ) + \mathrm { O } _ { 2 } ( g ) \quad \Delta H = 566.0 \mathrm { kJ }$, (3) $C(graphite) + O _ { 2 } ( g ) \rightarrow CO_2 ( g ) \quad \Delta H = - 393.5 \mathrm { kJ }$, (4) $2 \mathrm { CO } ( g ) \longrightarrow C(graphite) + \mathrm { CO } _ { 2 } ( g ) \quad \Delta H = - 172.5 \mathrm { kJ }$