Ch.10 - Gases

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970당신이 사용하는 게 아니라요?교과서 변경

Brown 15th Edition

Ch.10 - Gases

문제 102a

10장, 문제 102a

Assume that a single cylinder of an automobile engine has a volume of 524 cm3. a. If the cylinder is full of air at 74°C and 0.980 atm, how many moles of O2 are present? (The mole fraction of O2 in dry air is 0.2095.)

검증된 단계별 안내

Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature: \( T(K) = 74 + 273.15 \).

Use the ideal gas law equation \( PV = nRT \) to solve for the number of moles \( n \). Here, \( P \) is the pressure in atm, \( V \) is the volume in liters, \( R \) is the ideal gas constant \( 0.0821 \, \text{L atm/mol K} \), and \( T \) is the temperature in Kelvin.

Convert the volume from cm³ to liters by dividing by 1000: \( V(L) = \frac{524}{1000} \).

Substitute the values for \( P \), \( V \), \( R \), and \( T \) into the ideal gas law equation to find the total moles of gas \( n_{\text{total}} \).

Calculate the moles of \( O_2 \) by multiplying the total moles of gas by the mole fraction of \( O_2 \) in air: \( n_{O_2} = n_{\text{total}} \times 0.2095 \).

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주요 개념

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Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. Here, P is the pressure in atmospheres, V is the volume in liters, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(K·mol)), and T is the temperature in Kelvin. This law is essential for calculating the number of moles of gas in a given volume under specific conditions.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a specific component to the total number of moles of all components in the mixture. In this case, the mole fraction of O2 in dry air is given as 0.2095, indicating that 20.95% of the air is oxygen, which is crucial for determining the moles of O2 present in the cylinder.

Conversion of Units

In chemistry, it is often necessary to convert units to ensure consistency in calculations. For example, the volume of the cylinder is given in cm³, which must be converted to liters (1 L = 1000 cm³) for use in the Ideal Gas Law. Additionally, temperature must be converted from Celsius to Kelvin by adding 273.15. Proper unit conversion is vital for accurate results in gas calculations.

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교과서 질문

Carbon dioxide, which is recognized as the major contributor to global warming as a “greenhouse gas,” is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of CO2 added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about 6×106 tons of CO2 per year. a. Assuming ideal-gas behavior, 1.00 atm, and 27°C, calculate the volume of CO2 produced by this power plant.

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Assume that an exhaled breath of air consists of 74.8% N2, 15.3% O2, 3.7% CO2, and 6.2% water vapor. a. If the total pressure of the gases is 0.985 atm, calculate the partial pressure of each component of the mixture.

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Assume that an exhaled breath of air consists of 74.8% N₂, 15.3% O₂, 3.7% CO₂, and 6.2% water vapor. (c) How many grams of glucose (C₆H₁₂O₆) would need to be metabolized to produce this quantity of CO₂? (The chemical reaction is the same as that for combustion of C₆H₁₂O₆. See Section 3.2 and Problem 10.57.)

518

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교과서 질문

Nickel carbonyl, Ni(CO)4, is one of the most toxic substances known. The present maximum allowable concentration in laboratory air during an 8-h workday is 1 ppb (parts per billion) by volume, which means that there is one mole of Ni(CO)4 for every 109 moles of gas. Assume 24°C and 1.00 atm pressure. What mass of Ni(CO)4 is allowable in a laboratory room that is 12ft×20ft×9ft?

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교과서 질문

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