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 14th Edition

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Young & Freedman Calc 14th Edition

Ch 18: Thermal Properties of Matter

문제 1a

18장, 문제 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?

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.