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Chapter 7: Problem 117

Consider the reaction $$\mathrm{B}_{2} \mathrm{H}_{6}(g)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{B}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) \quad \Delta H=-2035 \mathrm{kJ}$$ Calculate the amount of heat released when \(54.0 \mathrm{g}\) of diborane is combusted.

Short Answer

Expert verified
The amount of heat released when \(54.0 \mathrm{g}\) of diborane is combusted is \(3973 \mathrm{kJ}\).

Step by step solution

01

Calculate the molar mass of diborane (B2H6)

To calculate the molar mass of diborane, we need to add up the atomic masses of its constituent elements. Look for the molar mass of boron (B) and hydrogen (H) in the periodic table: Molar mass of B = 10.81 g/mol Molar mass of H = 1.008 g/mol Now, let's calculate the molar mass of diborane: Molar mass of B2H6 = (2 x molar mass of B) + (6 x molar mass of H) Molar mass of B2H6 = (2 x 10.81 g/mol) + (6 x 1.008 g/mol) = 27.66 g/mol
02

Convert the mass of diborane into moles

To convert the mass of diborane into moles, we will use the following formula: moles of B2H6 = mass of B2H6 / molar mass of B2H6 Given mass of B2H6 = 54.0 g moles of B2H6 = 54.0 g / 27.66 g/mol = 1.95 mol
03

Determine the heat released per mole of diborane using the given ∆H value

The given ∆H value for the reaction is: ∆H = -2035 kJ/mol Since the ∆H value is negative, it indicates that the reaction is exothermic and releases heat. The -2035 kJ/mol value represents the heat released when 1 mole of diborane is combusted.
04

Calculate the total heat released for the given mass of diborane

To calculate the total heat released when 1.95 moles of diborane is combusted, multiply the moles of diborane by the heat released per mole of diborane: Total heat released = moles of B2H6 x ∆H Total heat released = 1.95 mol x -2035 kJ/mol = -3973 kJ Therefore, the amount of heat released when 54.0 g of diborane is combusted is 3973 kJ.

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Most popular questions from this chapter

Are the following processes exothermic or endothermic? a. When solid \(\mathrm{KBr}\) is dissolved in water, the solution gets colder. b. Natural gas \(\left(\mathrm{CH}_{4}\right)\) is burned in a furnace. c. When concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is added to water, the solution gets very hot. d. Water is boiled in a teakettle.

On Easter Sunday, April \(3,1983,\) nitric acid spilled from a tank car near downtown Denver, Colorado. The spill was neutralized with sodium carbonate: $$2 \mathrm{HNO}_{3}(a q)+\mathrm{Na}_{2} \mathrm{CO}_{3}(s) \longrightarrow 2 \mathrm{NaNO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)$$ a. Calculate \(\Delta H^{\circ}\) for this reaction. Approximately \(2.0 \times\) \(10^{4}\) gal nitric acid was spilled. Assume that the acid was an aqueous solution containing \(70.0 \%\) HNO \(_{3}\) by mass with a density of \(1.42 \mathrm{g} / \mathrm{cm}^{3} .\) What mass of sodium carbonate was required for complete neutralization of the spill, and what quantity of heat was evolved? \((\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{NaNO}_{3}(a q)=-467 \mathrm{kJ} / \mathrm{mol})\) b. According to The Denver Post for April \(4,1983,\) authorities feared that dangerous air pollution might occur during the neutralization. Considering the magnitude of \(\Delta H^{\circ}\) what was their major concern?

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