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Chapter 5: Problem 47

A 2.10-L vessel contains \(4.65 \mathrm{~g}\) of a gas at \(1.00 \mathrm{~atm}\) and \(27.0^{\circ} \mathrm{C}\). (a) Calculate the density of the gas in grams per liter. (b) What is the molar mass of the gas?

Short Answer

Expert verified
The density of the gas in the container is 2.21 g/L and the molar mass of the gas is 54.70 g/mol.

Step by step solution

01

Calculation of Number of Moles

To calculate the number of moles of the gas, we first need to convert the temperature from degrees Celsius to Kelvin. This is done using the formula: Kelvin = Celsius + 273.15. Thus, the temperature \(27.0^{\circ} C\) is equal to \(27.0 + 273.15 = 300.15 K\). Then, applying the ideal gas law, which is \(PV=nRT\), where \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin. We can solve for \(n\). For this problem \(P=1.00 atm\), \(V=2.10 L\), \(R=0.0821 L.atm/(mol.K)\), and \(T= 300.15 K\. Solving for \(n\), we have \(n = PV / RT = (1.00 atm * 2.10 L) / (0.0821 L.atm/(mol.K) * 300.15 K) = 0.085 moles\)
02

Calculating the Density

Density (\(d\)) is defined as mass per volume, given by the formula \(d = mass / volume\). Using the given mass of 4.65g and the volume of 2.10L, the density is therefore \(d = 4.65 g / 2.10 L = 2.21 g/L\)
03

Calculating the Molar Mass

Molar mass is defined as mass in gram divided by number of moles. Using the given mass of 4.65g and the calculated number of moles from Step 1 (0.085 moles), the molar mass is therefore \(Molar Mass = 4.65g / 0.085 moles = 54.70 g/mol\)

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Most popular questions from this chapter

In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at \(43^{\circ} \mathrm{C}\) : $$\mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(g)$$ This reaction separates nickel from other solid impurities. (a) Starting with \(86.4 \mathrm{~g}\) of \(\mathrm{Ni}\), calculate the pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in a container of volume \(4.00 \mathrm{~L}\). (Assume the above reaction goes to completion.) (b) On further heating the sample above \(43^{\circ} \mathrm{C}\), it is observed that the pressure of the gas increases much more rapidly than predicted based on the ideal gas equation. Explain.

The temperature of \(2.5 \mathrm{~L}\) of a gas initially at STP is increased to \(250^{\circ} \mathrm{C}\) at constant volume. Calculate the final pressure of the gas in atm.

Estimate the distance (in nanometers) between molecules of water vapor at \(100^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm}\). Assume ideal behavior. Repeat the calculation for liquid water at \(100^{\circ} \mathrm{C}\), given that the density of water is \(0.96 \mathrm{~g} / \mathrm{cm}^{3}\) at that temperature. Comment on your results. (Assume water molecule to be a sphere with a diameter of \(0.3 \mathrm{nm} .\) )

Calculate the mass in grams of hydrogen chloride produced when \(5.6 \mathrm{~L}\) of molecular hydrogen measured at STP react with an excess of molecular chlorine gas.

The pressure of \(6.0 \mathrm{~L}\) of an ideal gas in a flexible container is decreased to one-third of its original pressure, and its absolute temperature is decreased by one-half. What is the final volume of the gas?
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