Question

If oxygen gas in a steel container is at a pressure of 5.00 atm, what is the pressure expressed in each of the following units? (a) psi (b) \(\mathrm{cm} \mathrm{Hg}\)

Short answer

5 atm is equivalent to 73.48 psi and 380 cm Hg.

Step-by-step solution

Identify the Conversion factor for atm to psi

To convert pressure from atm to psi, we use the conversion factor that 1 atm is equivalent to 14.696 psi.

Convert pressure from atm to psi

Multiply the pressure in atm by the conversion factor to find the pressure in psi. \[ P_{\text{psi}} = 5.00 \, \text{atm} \times 14.696 \, \frac{\text{psi}}{\text{atm}} \]This calculation gives you the pressure in psi.

Calculate the pressure in psi

Perform the multiplication: \[ P_{\text{psi}} = 5.00 \times 14.696 = 73.48 \, \text{psi} \]So, the pressure in psi is 73.48.

Identify the Conversion factor for atm to cm Hg

To convert pressure from atm to cm Hg, we use the equivalence that 1 atm is approximately equal to 76 cm Hg.

Convert pressure from atm to cm Hg

Multiply the pressure in atm by the conversion factor to find the pressure in cm Hg. \[ P_{\text{cm Hg}} = 5.00 \, \text{atm} \times 76 \, \frac{\text{cm Hg}}{\text{atm}} \]This will give the pressure in cm Hg.

Calculate the pressure in cm Hg

Perform the multiplication: \[ P_{\text{cm Hg}} = 5.00 \times 76 = 380 \, \text{cm Hg} \]Thus, the pressure in cm Hg is 380.

Key concepts

atm to psi conversion

Pressure conversion is a vital concept in science and engineering because different experiments and industries often use specific pressure units that need to be interchangeable based on requirements. When you need to convert from atmospheric pressure (atm) to pounds per square inch (psi), you must use a specific conversion factor.

This conversion factor stems from the definition that 1 atm equals 14.696 psi. **Why is this conversion necessary?** Atm is a common unit used in chemistry, whereas psi is frequently used in engineering and other practical applications.

To perform the conversion, multiply the pressure value in atm by the conversion factor, 14.696 psi/atm. For instance, for 5.00 atm, the conversion to psi would be:

• Multiply 5.00 atm by 14.696 psi/atm.
• The result is 73.48 psi.

Now, you have successfully converted from atm to psi, making it easier to apply this pressure in different contexts.

atm to cm Hg conversion

When we speak about atmospheric pressure to centimeters of mercury (cm Hg) conversion, it involves the historical context and practical usage in environmental science and medicine. cm Hg is derived from the height of a column of mercury that the same pressure supports.

So, to convert atm to cm Hg, knowing that 1 atm equals approximately 76 cm Hg is crucial. This value arises because the atmosphere can support a column of mercury approximately 76 centimeters high. **How do you carry out this conversion?** Just multiply the number of atm you have by 76 cm Hg/atm.

For example, if you have a pressure of 5.00 atm and need it in cm Hg:

• Multiply 5.00 atm by 76 cm Hg/atm.
• The result is 380 cm Hg.

This conversion is particularly important in meteorology and medical instruments like blood pressure devices.

pressure units

Pressure is described by many units because it represents force acting per unit area, and different fields utilize varying measurement standards based on convenience and historical factors. This diversity provides flexibility but might also require conversions.

Among many pressure units, some common ones include:

• Atmospheres (atm), widely used in chemistry.
• Pounds per square inch (psi), standard in engineering applications in the U.S.
• Centimeters of mercury (cm Hg), frequently found in medical settings like blood pressure measurement.

Understanding and converting between these units enables accurate scientific communication and application across various contexts. Each unit provides a unique perspective on the magnitude of pressure, allowing for improved precision and understanding depending on the situation.