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Chapter 5: Problem 72

A student adds 4.00 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
After the 4.00 g of dry ice sublimes, the volume of the balloon at STP (Standard Temperature and Pressure) will be approximately 2.04 L.

Step by step solution

01

Calculate the moles of CO2

First, we need to find the number of moles of CO2 using the given mass and molar mass of CO2. Molar mass of CO2: C = 12.01 g/mol O = 16.00 g/mol Molar mass of CO2 = 1 × C + 2 × O = 1 × 12.01 g/mol + 2 × 16.00 g/mol = 44.01 g/mol Given mass of CO2: 4.00 g Now, we can calculate the number of moles (n) of CO2: n = (given mass) / (molar mass) n = 4.00 g / 44.01 g/mol ≈ 0.0909 mol
02

Calculate the volume of the balloon using Ideal Gas Law

Now that we have the number of moles of CO2 and the conditions are at STP, we can use the Ideal Gas Law equation to find the volume of the balloon. At STP, Temperature (T) = 273.15 K Pressure (P) = 1 atm Ideal Gas Law equation: \(PV=nRT\) We want to find the volume (V). Rearrange the equation for solving 'V': V = (nRT) / P Put the values into the equation and solve for the volume (V): V = (0.0909 mol × 0.0821 L atm/mol K × 273.15 K) / (1 atm) V = 2.0434 L So, after all the dry ice sublimes, the volume of the balloon at STP would be approximately 2.04 L.

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Most popular questions from this chapter

\(\mathrm{N}_{2} \mathrm{O}\) is a gas commonly used to help sedate patients in medicine and dentistry due to its mild anesthetic and analgesic properties; it is also nonflammable. If a cylinder of \(\mathrm{N}_{2} \mathrm{O}\) is at 10.5 atm and has a volume of 5.00 \(\mathrm{L}\) at \(298 \mathrm{K},\) how many moles of \(\mathrm{N}_{2} \mathrm{O}\) gas are present? The gas from the cylinder is emptied into a large balloon at 745 torr. What is the volume of the balloon at 298 \(\mathrm{K}\) ?

A 2.50-L container is filled with 175 g argon. a. If the pressure is 10.0 atm, what is the temperature? b. If the temperature is 225 K, what is the pressure?

Do all the molecules in a 1 -mole sample of \(\mathrm{CH}_{4}(g)\) have the same kinetic energy at 273 \(\mathrm{K}\)? Do all molecules in a 1 -mole sample of \(\mathrm{N}_{2}(g)\) have the same velocity at 546 \(\mathrm{K}\) ? Explain.

A chemist weighed out 5.14 g of a mixture containing unknown amounts of \(\mathrm{BaO}(s)\) and \(\mathrm{CaO}(s)\) and placed the sample in a \(1.50-\mathrm{L}\) flask containing \(\mathrm{CO}_{2}(g)\) at $30.0^{\circ} \mathrm{C}\( and 750 . torr. After the reaction to form BaCO_ \)_{3}(s)$ and \(\mathrm{CaCO}_{3}(s)\) was completed, the pressure of \(\mathrm{CO}_{2}(g)\) remaining was 230 . torr. Calculate the mass percentages of \(\mathrm{CaO}(s)\) and \(\mathrm{BaO}(s)\) in the mixture.

A 20.0 -L stainless steel container at \(25^{\circ} \mathrm{C}\) was charged with 2.00 atm of hydrogen gas and 3.00 atm of oxygen gas. A spark ignited the mixture, producing water. What is the pressure in the tank at $25^{\circ} \mathrm{C}$ ? If the exact same experiment were performed, but the temperature was \(125^{\circ} \mathrm{C}\) instead of \(25^{\circ} \mathrm{C},\) what would be the pressure in the tank?
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