A concentration of 8.00 ×10^2 ppm by volume of CO is considered lethal to humans. Calculate the

step 1 Hello, so today we're going to be looking at a situation where we have a box like room with the

A concentration of 8.00 ×10^2 ppm by volume of CO is...

A concentration of $8.00 \times 10^{2}$ ppm by volume of $\mathrm{CO}$ is considered lethal to humans. Calculate the minimum mass of $\mathrm{CO}$ in grams that would become a lethal concentration in a closed room $17.6 \mathrm{~m}$ long, $8.80 \mathrm{~m}$ wide, and $2.64 \mathrm{~m}$ high. The temperature and pressure are $20.0^{\circ} \mathrm{C}$ and $756 \mathrm{mmHg}$, respectively.

Key Concepts

Parts per Million (PPM) as a Volume Fraction

PPM is a unit used to express very dilute concentrations of substances. When given as ppm by volume for gases, it indicates the ratio of the volume of a particular gas to the total volume of the gas mixture multiplied by one million. In solving problems like this, converting the ppm value to a fraction is essential for determining the proportion of the gas present in any given volume.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, is a fundamental relation in physical chemistry that links pressure, volume, temperature, and the number of moles of a gas. It is used to calculate the amount of substance (in moles) present in a defined space under specified conditions, thereby allowing one to work out how many moles of a gas correspond to a certain concentration in a container.

Unit Conversions

Accurate problem solving in gas law applications often requires converting units, such as pressure from mm Hg to atmospheres or temperature from degrees Celsius to Kelvin. These conversions are necessary because the gas constant R in the Ideal Gas Law is defined with specific units, ensuring consistency and correctness in calculations.

Molar Mass and Conversion from Moles to Mass

The molar mass of a substance is the mass of one mole of its molecules, expressed in grams per mole. After determining the number of moles of a gas using the Ideal Gas Law, multiplying by its molar mass allows one to convert this amount into grams, thereby linking the microscopic scale of molecules to measurable macroscopic quantities.

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