Answered

Gases are different from solids and liquids. In a sample of gas, the molecules are far apart. The gas molecules also move around and collide with each other as well as with the walls of the container. These collisions generate pressure. The pressure of a gas can be measured in different units. One convenient unit of measure is called the atmosphere (atm) because it is based on atmospheric pressure. At sea level, the average pressure is 1 atm. As you get higher in altitude, the pressure steadily drops until you leave the atmosphere, where the pressure is very close to 0 atm.

The table below shows the different commonly used units of measuring gas pressure. Use this table in the pressure unit conversions.

\begin{tabular}{|l|c|c|}
\hline
\multicolumn{1}{|c|}{Unit} & Abbreviation & 1 atm equivalent \\
\hline
atmosphere & atm & 1.00 atm (exact) \\
\hline
millimeters of mercury & mmHg & 760 mmHg \\
\hline
torr & torr & 760 torr \\
\hline
inches of mercury & in. Hg & [tex]$29.9$[/tex] in. Hg \\
\hline
\begin{tabular}{l}
pounds per square \\
inch (psi)
\end{tabular} & [tex]$lb/in.^2$[/tex] & [tex]$14.7 \, lb/in.^2$[/tex] \\
\hline
pascal & Pa & [tex]$101,325 \, Pa$[/tex] \\
\hline
\end{tabular}

Part A

Convert 1.20 atm of pressure to its equivalent in millimeters of mercury.
Express the pressure numerically in millimeters of mercury.

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Part B

The pressure in car tires is often measured in pounds per square inch ([tex]$lb/in.^2$[/tex]). Suppose a tire has a pressure of [tex]$27.5 \, lb/in.^2$[/tex]. Convert [tex]$27.5 \, lb/in.^2$[/tex] to atmospheres.
Express the pressure numerically in atmospheres.

[tex]\[\boxed{\text{Submit}}\][/tex]



Answer :

GinnyAnswer
Certainly! Let's go through the problem step by step.

### Part A: Convert 1.20 atm to millimeters of mercury (mmHg)

To convert a pressure from atmospheres (atm) to millimeters of mercury (mmHg), we need to know the conversion factor between these two units. From the provided table, we know that:

[tex]\[ 1 \text{ atm} = 760 \text{ mmHg} \][/tex]

We are given a pressure of 1.20 atm, and we need to convert it to mmHg using the conversion factor.

[tex]\[ \text{Pressure in mmHg} = \text{Pressure in atm} \times 760 \text{ mmHg/atm} \][/tex]

Substituting our given value:

[tex]\[ \text{Pressure in mmHg} = 1.20 \text{ atm} \times 760 \text{ mmHg/atm} \][/tex]

[tex]\[ \text{Pressure in mmHg} = 912.0 \text{ mmHg} \][/tex]

So, 1.20 atm is equivalent to 912.0 mmHg.

### Part B: Convert 27.5 lb/in² to atmospheres (atm)

To convert pressure from pounds per square inch (psi) to atmospheres (atm), we need to know the conversion factor between these two units. From the table, we see that:

[tex]\[ 1 \text{ atm} = 14.7 \text{ lb/in}^2 \][/tex]

We are given a pressure of 27.5 lb/in² and we need to convert it to atmospheres. To do so, we divide the pressure in psi by the conversion factor (14.7 lb/in² per atm):

[tex]\[ \text{Pressure in atm} = \frac{\text{Pressure in psi}}{14.7 \text{ lb/in}^2/\text{atm}} \][/tex]

Substituting our given value:

[tex]\[ \text{Pressure in atm} = \frac{27.5 \text{ lb/in}^2}{14.7 \text{ lb/in}^2/\text{atm}} \][/tex]

[tex]\[ \text{Pressure in atm} \approx 1.870748299319728 \text{ atm} \][/tex]

So, 27.5 lb/in² is approximately equivalent to 1.87075 atm.

### Summary

- Part A: 1.20 atm is converted to 912.0 mmHg.
- Part B: 27.5 lb/in² is converted to approximately 1.87075 atm.