A 20.020.0-L tank contains 4.86×10−44.86\$$times10^{-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?

Ch 18: Thermal Properties of Matter

Young & Freedman Calc - University Physics 15th Edition

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Young & Freedman Calc 15th Edition

Ch 18: Thermal Properties of Matter

Problem 1a

Chapter 18, Problem 1a

A $20.0$ -L tank contains $4.86 \times 10^{- 4}$ kg of helium at $18.0$ °C. The molar mass of helium is $4.00$ g/mol. How many moles of helium are in the tank?

Verified step by step guidance

First, convert the mass of helium from kilograms to grams. Since 1 kg = 1000 g, multiply 4.86 * 10^-4 kg by 1000 to get the mass in grams.

Next, use the molar mass of helium to find the number of moles. The molar mass of helium is 4.00 g/mol. Use the formula: $ \text{Number of moles} = \frac{\text{mass in grams}}{\text{molar mass}} $.

Substitute the mass of helium in grams and the molar mass into the formula to calculate the number of moles.

Ensure that the units are consistent and correctly cancel out, leaving you with the number of moles.

Review the calculation to ensure accuracy and understanding of the relationship between mass, molar mass, and moles.

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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 is a fundamental equation in physics that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as 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 in Kelvin. This law is crucial for calculating the number of moles of a gas when other properties are known.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is used to convert between the mass of a substance and the number of moles. For helium, the molar mass is 4.00 g/mol, which allows us to determine the number of moles from a given mass of helium by dividing the mass by the molar mass.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set of units. In this context, converting the mass of helium from kilograms to grams is necessary to use the molar mass in calculations. Understanding how to convert units ensures accurate calculations and is essential for solving problems involving different measurement systems.

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Unit Conversions

Related Practice

Textbook Question

Helium gas with a volume of $3.20$ L, under a pressure of $0.180$ atm and at $41.0$ °C, is warmed until both pressure and volume are doubled. What is the final temperature?

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Textbook Question

A $20.0$ -L tank contains $4.86$\times$10^{-4}$ kg of helium at $18.0$ °C. The molar mass of helium is $4.00$ g/mol. What is the pressure in the tank, in pascals and in atmospheres?

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Textbook Question

Helium gas with a volume of $3.20$ L, under a pressure of $0.180$ atm and at $41.0$ °C, is warmed until both pressure and volume are doubled. How many grams of helium are there? The molar mass of helium is $4.00$ g/mol.

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A 20.020.0-L tank contains 4.86×10−44.86\(\times\)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?

Verified video answer for a similar problem:

Key Concepts

Ideal Gas Law

Molar Mass

Unit Conversion

A $20.0$ -L tank contains $4.86 \times 10^{- 4}$ kg of helium at $18.0$ °C. The molar mass of helium is $4.00$ g/mol. How many moles of helium are in the tank?