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Chapter 5: Problem 40

Calculate its volume (in liters) of \(88.4 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) at STP.

Short Answer

Expert verified
The volume of 88.4 g of \(\mathrm{CO}_{2}\) at STP is 44.8 L.

Step by step solution

01

Determining the molar mass

First, we need to determine the molar mass of carbon dioxide (\( \mathrm{CO}_{2}\)), in terms of grams per mole (\( g/mol \)). Carbon has a molar mass of 12.01 g/mol and oxygen has a molar mass of 16.00 g/mol. Since there are two oxygen atoms for every one carbon atom in \( \mathrm{CO}_{2}\), the molar mass \( M \) is \( 12.01 g/mol + 2 * 16.00 g/mol = 44.01 g/mol \).
02

Calculating number of moles

Next, divide the mass given in the problem by the molar mass of \( \mathrm{CO}_{2}\) to find the number of moles \( n \). We know the mass \( m \) is 88.4 g and the molar mass \( M \) is 44.01 g/mol, so the number of moles \( n \) is \( m / M = 88.4 \, g / 44.01 \, g/mol = 2 \, moles \).
03

Calculating volume

Finally, multiply the number of moles of \( \mathrm{CO}_{2}\) by the volume that one mole of any gas occupies at STP. We know that one mole of any gas occupies a volume of 22.4 liters at STP. So, the volume \( V \) is \( n * 22.4 \, L/mol = 2 \, moles * 22.4 \, L/mol = 44.8 \, L \). So, 88.4 g of \( \mathrm{CO}_{2}\) at STP occupies a volume of 44.8 liters.

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Most popular questions from this chapter

A certain hydrate has the formula \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\). A quantity of \(54.2 \mathrm{~g}\) of the compound is heated in an oven to drive off the water. If the steam generated exerts a pressure of 24.8 atm in a \(2.00-\mathrm{L}\) container \(\mathrm{at}\) \(120^{\circ} \mathrm{C},\) calculate \(x\)

Which of the following has a greater mass: a sample of air of volume \(V\) at a certain temperature \(T\) and pressure \(P\) or a sample of air plus water vapor having the same volume and at the same temperature and pressure?

Under the same conditions of temperature and pressure, which of the following gases would behave most ideally: Ne, \(\mathrm{N}_{2}\), or \(\mathrm{CH}_{4}\) ? Explain.

What are standard temperature and pressure (STP)? What is the significance of STP in relation to the volume of 1 mole of an ideal gas?

Ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) burns in air: $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) $$ Balance the equation and determine the volume of air in liters at \(35.0^{\circ} \mathrm{C}\) and \(790 \mathrm{mmHg}\) required to burn \(227 \mathrm{~g}\) of ethanol. Assume that air is 21.0 percent \(\mathrm{O}_{2}\) by volume.
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