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Chapter 8: Problem 66

A student adds \(4.00 \mathrm{g}\) of dry ice (solid \(\mathrm{CO}_{2}\) ) to an empty balloon. What will be the volume of the balloon at STP after all the dry ice sublimes (converts to gaseous \(\mathrm{CO}_{2}\) )?

Short Answer

Expert verified
The volume of the balloon after all the dry ice sublimes will be approximately \(2.1 \mathrm{L}\) at STP.

Step by step solution

01

Calculate moles of CO₂

To calculate the moles of CO₂, we need to use the given mass and the molar mass of CO₂. The molar mass of CO₂ is 44.01 g/mol. Moles of CO₂ = Mass of CO₂ / Molar mass of CO₂ n = 4.00 g / 44.01 g/mol n ≈ 0.0909 mol
02

Use Ideal Gas Law to find Volume

Now we can use the ideal gas law to find the volume, V. At STP, the temperature, T, is 0°C (or 273.15 K) and the pressure, P, is 1 atm. We also know the gas constant, R: 0.0821 L*atm/(mol*K). The equation is written as: PV = nRT First, we should isolate the volume (V) on one side of the equation: V = nRT / P Now, we can plug in the values we know: V = (0.0909 mol) (0.0821 L*atm/(mol*K)) (273.15 K) / (1 atm) V ≈ 2.05 L
03

Round the answer

Finally, we should round the answer to an appropriate number of significant figures. In this case, 2 significant figures are appropriate, since the mass of dry ice given in the problem has 2 significant figures: V ≈ 2.1 L #Answer# So, the volume of the balloon after all the dry ice sublimes will be approximately 2.1 liters at STP.

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Most popular questions from this chapter

At STP, \(1.0 \mathrm{L}\) \(Br\) \(_{2}\) reacts completely with \(3.0 \mathrm{L} \mathrm{F}_{2}\), producing \(2.0 \mathrm{L}\) of a product. What is the formula of the product? (All substances are gases.)

Ideal gas particles are assumed to be volumeless and to neither attract nor repel each other. Why are these assumptions crucial to the validity of Dalton's law of partial pressures?

An ideal gas is contained in a cylinder with a volume of \(5.0 \times 10^{2} \mathrm{mL}\) at a temperature of \(30 .^{\circ} \mathrm{C}\) and a pressure of \(710.\) torr. The gas is then compressed to a volume of \(25 \mathrm{mL}\) and the temperature is raised to \(820 .^{\circ} \mathrm{C}\). What is the new pressure of the gas?

An important process for the production of acrylonitrile \(\left(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}\right)\) is given by the following equation: $$2 \mathrm{C}_{3} \mathrm{H}_{6}(g)+2 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$ A \(150 .\)-\(\mathrm{L}\)reactor is charged to the following partial pressures at \(25^{\circ} \mathrm{C}:\) $$\begin{aligned}P_{\mathrm{C}, \mathrm{H}_{6}} &=0.500 \mathrm{MPa} \\\P_{\mathrm{NH}_{3}} &=0.800 \mathrm{MPa} \\\P_{\mathrm{O}_{2}} &=1.500 \mathrm{MPa}\end{aligned}$$ What mass of acrylonitrile can be produced from this mixture \(\left(\mathrm{MPa}=10^{6} \mathrm{Pa}\right) ?\)

Silane, \(\mathrm{SiH}_{4},\) is the silicon analogue of methane, \(\mathrm{CH}_{4} .\) It is prepared industrially according to the following equations: $$\begin{aligned} \mathrm{Si}(s)+3 \mathrm{HCl}(g) & \longrightarrow \mathrm{HSiCl}(i)+\mathrm{H}_{2}(g) \\\4 \mathrm{HSiCl}_{3}(l) & \longrightarrow \mathrm{SiH}_{4}(g)+3 \mathrm{SiCl}_{4}(l)\end{aligned}$$ a. If \(156 \mathrm{mL} \mathrm{HSiCl}_{3}(d=1.34 \mathrm{g} / \mathrm{mL})\) is isolated when \(15.0 \mathrm{L}\) HCl at \(10.0\) atm and \(35^{\circ} \mathrm{C}\) is used, what is the percent yield of HSiCl_? b. When \(156 \mathrm{mL}\) \(HSiCl_{3}\)is heated, what volume of \(\mathrm{SiH}_{4}\) at \(10.0\) atm and \(35^{\circ} \mathrm{C}\) will be obtained if the percent yield of the reaction is \(93.1 \% ?\)
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