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Chapter 10: Problem 79

Do all gases at the same pressure and temperature have the same density? Explain your answer.

Short Answer

Expert verified
Explain your answer. Answer: No, not all gases at the same pressure and temperature have the same density. The density of a gas is given by the formula 蟻 = PM/(RT), where P is pressure, M is molar mass, R is the gas constant, and T is temperature. Different gases have different molar masses, which ultimately affects their densities even when they have the same pressure and temperature.

Step by step solution

01

Recall the Ideal Gas Equation

The ideal gas equation is given by: PV = nRT where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
02

Density Formula

We know that density (蟻) is defined as mass (m) per unit volume (V). The formula for density is: 蟻 = m/V
03

Relating Ideal Gas Equation with Density

We can rewrite the ideal gas equation in terms of mass (m) and molar mass (M) instead of the number of moles (n). This helps us relate it to the density formula. Knowing that n = m/M, we can replace n in the ideal gas equation: PV = (m/M)RT Now, we can isolate the mass-to-volume ratio (m/V), which is the density (蟻): 蟻 = PM/(RT)
04

Comparing Densities

Now we can see that the density of a gas is given by the formula 蟻 = PM/(RT). If two different gases are at the same pressure (P) and temperature (T), we need to look at their molar masses (M) to determine their densities.
05

Conclusion

In conclusion, not all gases at the same pressure and temperature have the same density because their densities are affected by their molar masses (M). Different gases have different molar masses, which ultimately affects their densities even when they have the same pressure and temperature.

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Most popular questions from this chapter

Which noble gas effuses 3.2 times faster than argon at \(0^{\circ} \mathrm{C}\)?

A gas mixture contains \(7.0 \mathrm{g} \mathrm{N}_{2}, 2.0 \mathrm{g} \mathrm{H}_{2},\) and \(16.0 \mathrm{g} \mathrm{CH}_{4}\) What is the mole fraction of \(\mathrm{H}_{2}\) in the mixture?

How does the density of a gas sample change when (a) its pressure is increased and (b) its temperature is decreased?

Which noble gas is expected to deviate the most from ideal behavior in a graph of PV/RT versus \(P ?\)

Suppose the temperature of the gas in Figure \(\mathrm{P} 10.2(\mathrm{b})\) increases from \(200 \mathrm{K}\) to \(400 \mathrm{K}\) but that the pressure on the piston remains constant. Does the position of the piston change? If so, by how much does the volume of the gas change?
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