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Ch 18: Thermal Properties of Matter
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 18, Problem 2b

Helium gas with a volume of 3.203.20 L, under a pressure of 0.1800.180 atm and at 41.041.0°C, is warmed until both pressure and volume are doubled. How many grams of helium are there? The molar mass of helium is 4.004.00 g/mol.

Verified step by step guidance
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Start by converting the temperature from Celsius to Kelvin. The formula for conversion is: T=T+273.15. So, the initial temperature is 41.0+273.15 K.
Use the ideal gas law to find the number of moles of helium. The ideal gas law is given by: PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. Rearrange the formula to solve for n: n=PVRT.
Substitute the known values into the rearranged ideal gas law equation. Use R = 0.0821 L atm/mol K for the ideal gas constant. The initial conditions are P = 0.180 atm, V = 3.20 L, and T = 314.15 K.
Calculate the number of moles of helium using the substituted values. This will give you n, the number of moles of helium gas present under the initial conditions.
Finally, convert the number of moles to grams using the molar mass of helium. The formula is: m=n×M, where M is the molar mass of helium (4.00 g/mol). This will give you the mass of helium in grams.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law, PV = nRT, relates the pressure (P), volume (V), and temperature (T) of a gas to the number of moles (n) and the ideal gas constant (R). It is essential for calculating the amount of gas when conditions change, such as pressure and volume doubling, as in this problem.
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Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). For helium, the molar mass is 4.00 g/mol, which is crucial for converting moles of helium calculated from the Ideal Gas Law into grams, answering the question about the mass of helium.
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Temperature Conversion

Temperature in gas law calculations must be in Kelvin. To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature. This conversion is necessary to accurately apply the Ideal Gas Law, as the initial temperature given is in Celsius (41.0°C).
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Related Practice
Textbook Question

A large cylindrical tank contains 0.7500.750 m3 of nitrogen gas at 2727°C and 7.50×1037.50\(\times\)10^3 Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.4100.410 m3 and the temperature is increased to 157157°C?

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Textbook Question

Helium gas with a volume of 3.203.20 L, under a pressure of 0.1800.180 atm and at 41.041.0°C, is warmed until both pressure and volume are doubled. What is the final temperature?

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Textbook Question

A 20.020.0-L tank contains 4.86×1044.86\(\times\)10^{-4} kg of helium at 18.018.0°C. The molar mass of helium is 4.004.00 g/mol. How many moles of helium are in the tank?

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Textbook Question

A 20.020.0-L tank contains 4.86×1044.86\(\times\)10^{-4} kg of helium at 18.018.0°C. The molar mass of helium is 4.004.00 g/mol. What is the pressure in the tank, in pascals and in atmospheres?

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Textbook Question

A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.1100.110 m3 of air at a pressure of 0.3550.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.3900.390 m3. If the temperature remains constant, what is the final value of the pressure?

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Textbook Question

You have several identical balloons. You experimentally determine that a balloon will break if its volume exceeds 0.9000.900 L. The pressure of the gas inside the balloon equals air pressure (1.001.00 atm). If the air inside the balloon is at a constant 22.022.0°C and behaves as an ideal gas, what mass of air can you blow into one of the balloons before it bursts?

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