/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 48 A constant volume gas thermomete... [FREE SOLUTION] | 91影视

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Chapter 13: Problem 48

A constant volume gas thermometer containing helium is immersed in boiling ammonia \(\left(-33^{\circ} \mathrm{C}\right)\) and the pressure is read once equilibrium is reached. The thermometer is then moved to a bath of boiling water \(\left(100.0^{\circ} \mathrm{C}\right) .\) After the manometer was adjusted to keep the volume of helium constant, by what factor was the pressure multiplied?

Short Answer

Expert verified
Answer: The pressure was multiplied by a factor of approximately 1.55.

Step by step solution

01

Understand the given information

We are given: - Temperature of boiling ammonia = \(-33^{\circ} \mathrm{C}\) - Temperature of boiling water = \(100.0^{\circ} \mathrm{C}\) - The volume of the gas remains constant.
02

Convert the temperatures to Kelvin scale

The temperatures given are in Celsius. We need to convert them to Kelvin to work with the ideal gas law. - Temperature of boiling ammonia in Kelvin = \((-33+273) K = 240 K\) - Temperature of boiling water in Kelvin = \((100+273) K = 373 K\)
03

Use the ideal gas law

The ideal gas law states: \(PV = nRT\) Since the volume and the amount of gas are constant, we can compare the pressures and temperatures as follows: - \(P_1/T_1 = P_2/T_2\) We need to find the factor by which the pressure was multiplied, which is \(P_2/P_1\)
04

Solve for the pressure factor

Now we can solve for the pressure factor (P2/P1) as follows: $$ \frac{P_2}{P_1}=\frac{T_2}{T_1}=\frac{373 \mathrm{K}}{240 \mathrm{K}} $$
05

Calculate the pressure factor

To find the factor by which the pressure was multiplied, divide the temperatures in Kelvin: $$ \frac{P_2}{P_1}=\frac{373}{240} \approx 1.55 $$ The pressure was multiplied by a factor of approximately 1.55.

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Most popular questions from this chapter

A certain acid has a molecular mass of 63 u. By mass, it consists of \(1.6 \%\) hydrogen, \(22.2 \%\) nitrogen, and \(76.2 \%\) oxygen. What is the chemical formula for this acid?
What are the rms speeds of helium atoms, and nitrogen, hydrogen, and oxygen molecules at \(25^{\circ} \mathrm{C} ?\)
A cylinder with an interior cross-sectional area of \(70.0 \mathrm{cm}^{2}\) has a moveable piston of mass \(5.40 \mathrm{kg}\) at the top that can move up and down without friction. The cylinder contains $2.25 \times 10^{-3} \mathrm{mol}\( of an ideal gas at \)23.0^{\circ} \mathrm{C} .$ (a) What is the volume of the gas when the piston is in equilibrium? Assume the air pressure outside the cylinder is 1.00 atm. (b) By what factor does the volume change if the gas temperature is raised to \(223.0^{\circ} \mathrm{C}\) and the piston moves until it is again in equilibrium?
An ideal gas that occupies \(1.2 \mathrm{m}^{3}\) at a pressure of $1.0 \times 10^{5} \mathrm{Pa}\( and a temperature of \)27^{\circ} \mathrm{C}$ is compressed to a volume of \(0.60 \mathrm{m}^{3}\) and heated to a temperature of \(227^{\circ} \mathrm{C} .\) What is the new pressure?
Agnes Pockels \((1862-1935)\) was able to determine Avogadro's number using only a few household chemicals, in particular oleic acid, whose formula is \(\mathrm{C}_{18} \mathrm{H}_{34} \mathrm{O}_{2}\) (a) What is the molar mass of this acid? (b) The mass of one drop of oleic acid is \(2.3 \times 10^{-5} \mathrm{g}\) and the volume is $2.6 \times 10^{-5} \mathrm{cm}^{3} .$ How many moles of oleic acid are there in one drop? (c) Now all Pockels needed was to find the number of molecules of oleic acid. Luckily, when oleic acid is spread out on water, it lines up in a layer one molecule thick. If the base of the molecule of oleic acid is a square of side \(d\), the height of the molecule is known to be \(7 d .\) Pockels spread out one drop of oleic acid on some water, and measured the area to be \(70.0 \mathrm{cm}^{2}\) Using the volume and the area of oleic acid, what is \(d ?\) (d) If we assume that this film is one molecule thick, how many molecules of oleic acid are there in the drop? (e) What value does this give you for Avogadro's number?
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