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.)

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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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Key Concepts

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

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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