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Ch 18: Thermal Properties of Matter
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Capitolo 18, Problema 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.

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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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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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Ideal Gases and the Ideal Gas Law

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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Mass Spectrometers

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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Unit Conversions
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