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Chapter 7: Problem 33

The enthalpy of sublimation ( solid \(\rightarrow\) gas) for dry ice (i.e., \(\mathrm{CO}_{2}\) ) is \(\Delta H_{\mathrm{sub}}^{\circ}=571 \mathrm{kJ} / \mathrm{kg}\) at \(-78.5^{\circ} \mathrm{C} .\) If \(125.0 \mathrm{J}\) of heat is transferred to a block of dry ice that is \(-78.5^{\circ} \mathrm{C},\) what volume of \(\mathrm{CO}_{2} \operatorname{gas}(d=1.98 \mathrm{g} / \mathrm{L})\) will be generated?

Short Answer

Expert verified
The volume of \( CO_2 \) gas produced is \( 0.111 \ L \)

Step by step solution

01

Identify the known variables

The given known variables in this problem are: enthalpy of sublimation \(\Delta H_{sub}^\circ = 571 \ kJ/kg\), the mass of dry ice that is -78.5 C, \( m = 125.0 \ J \), the heat is transferred to a block of dry ice, \( q = 125.0 \ J \), the density of \( CO_2 \) gas, \( d = 1.98 \ g/L \)
02

Convert the joules to kJ

The given heat \( q \) is in joules, however, the given enthalpy of sublimation \(\Delta H_{sub}\) is in kJ/kg. Therefore the given heat should be converted to kJ in order to be compatible for the following calculations. \( 1 \ kJ = 1000 \ J\), therefore, \( 125.0 \ J = 125.0 / 1000 \ kJ = 0.125 \ kJ \)
03

Calculate the mass of \( CO_2 \)

The formula for the heat transfer in a change of state is given as \( q = m \delta H \). Solving for \( m \), the mass, gives, \( m = q / \delta H = 0.125 \ kJ / 571 \ kJ/kg = 2.19 x 10^-4 \ kg \). Since the amount required is in grams, this mass should be converted to grams. \( 1 \ kg = 1000 \ g \), so \( 2.19 x 10^-4 \ kg = 2.19 x 10^-4 x 1000 \ g = 0.219 \ g \)
04

Calculate the volume of \( CO_2 \) gas

Density, \( d \), is defined as mass over volume or \( d = m / V \). Solving for \( V \), the volume, gives \( V = m / d = 0.219 \ g / 1.98 \ g/L = 0.111 \ L \)

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Most popular questions from this chapter

How much heat, in kilojoules, is evolved in the complete combustion of (a) \(1.325 \mathrm{g} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})\) at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{atm} ;\) (b) \(28.4 \mathrm{L} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})\) at \(\mathrm{STP} ;(\mathrm{c})\) \(12.6 \mathrm{LC}_{4} \mathrm{H}_{10}(\mathrm{g})\) at \(23.6^{\circ} \mathrm{C}\) and \(738 \mathrm{mmHg} ?\) Assume that the enthalpy change for the reaction does not change significantly with temperature or pressure. The complete combustion of butane, \(\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g}),\) is represented by the equation $$\begin{array}{r} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})+\frac{13}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{CO}_{2}(\mathrm{g})+5 \mathrm{H}_{2} \mathrm{O}(1) \\ \Delta H^{\circ}=-2877 \mathrm{kJ} \end{array}$$

Calculate the quantity of work associated with a \(3.5 \mathrm{L}\) expansion of a gas \((\Delta V)\) against a pressure of \(748 \space\mathrm{mmHg}\) in the units (a) atm \(\mathrm{L} ;\) (b) joules (J); (c) calories (cal).

Determine \(\Delta H^{\circ}\) for this reaction from the data below. \(\mathrm{N}_{2} \mathrm{H}_{4}(1)+2 \mathrm{H}_{2} \mathrm{O}_{2}(1) \longrightarrow \mathrm{N}_{2}(\mathrm{g})+4 \mathrm{H}_{2} \mathrm{O}(1)\) $$\begin{array}{r} \mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{l})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{N}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \\ \Delta H^{\circ}=-622.2 \mathrm{kJ} \end{array}$$ $$\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \quad \Delta H^{\circ}=-285.8 \mathrm{kJ}$$ $$\mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}_{2}(1) \quad \Delta H^{\circ}=-187.8 \mathrm{kJ}$$

The heat of solution of \(\mathrm{KI}(\mathrm{s})\) in water is \(+20.3 \mathrm{kJ} / \mathrm{mol}\) KI. If a quantity of KI is added to sufficient water at \(23.5^{\circ} \mathrm{C}\) in a Styrofoam cup to produce \(150.0 \mathrm{mL}\) of 2.50 M KI, what will be the final temperature? (Assume a density of \(1.30 \mathrm{g} / \mathrm{mL}\) and a specific heat of \(2.7 \mathrm{Jg}^{-1}\) \(\left.^{\circ} \mathrm{C}^{-1} \text {for } 2.50 \mathrm{M} \mathrm{KI} .\right)\)

What is the change in internal energy of a system if the system (a) absorbs \(58 \mathrm{J}\) of heat and does \(58 \mathrm{J}\) of work; (b) absorbs 125 J of heat and does 687 J of work; (c) evolves 280 cal of heat and has 1.25 kJ of work done on it?
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