Problem 10 - Analytical Chemistry

Question

Gas reduction valves used on gas tanks in gas chromatography usually give the pressure in psig (pounds per square inch above atmospheric pressure). Given that atmospheric pressure (760 torr) is 14.7 psi, calculate the inlet pressure to the gas chromatograph in torr, for 40.0 psig, if the ambient pressure is 745 torr.

Step-by-Step Solution

Answer

The inlet pressure to the gas chromatograph is approximately 2814.61 torr.

Step 1: Understand the Given Values

We know that the pressure given is 40.0 psig. Atmospheric pressure is given in torr as 745 torr in this specific case. We also have the standard conversion factor: 1 atm is 14.7 psi and 760 torr.

Step 2: Convert psig to psi Absolute Pressure

To convert from psig (pounds per square inch gauge) to psi (pounds per square inch absolute), add the ambient pressure in psi to the psig value.Given that atmospheric pressure at standard conditions (14.7 psi) corresponds to 760 torr, we can find the ambient pressure in psi by using a ratio:\[ \text{ambient pressure in psi} = \left( \frac{745 \text{ torr}}{760 \text{ torr}} \right) \times 14.7 \text{ psi} \]Calculating this, \[ \text{ambient pressure in psi} \approx 14.42 \text{ psi} \]So, the absolute pressure in psi is:\[ 40.0 \text{ psig} + 14.42 \text{ psi} = 54.42 \text{ psi} \]

Step 3: Convert Absolute Pressure from psi to torr

To convert absolute pressure from psi to torr, we use the conversion:\[ 1 \text{ psi} = \frac{760 \text{ torr}}{14.7 \text{ psi}} \]Thus, to convert 54.42 psi to torr:\[ 54.42 \text{ psi} \times \frac{760 \text{ torr}}{14.7 \text{ psi}} \approx 2814.61 \text{ torr} \]

Step 4: Confirm the Calculation

Re-check the calculations for any mathematical errors and make sure all conversion factors are correctly applied. Ensure that we have followed through all necessary conversions step by step accurately to arrive at the correct value: 2814.61 torr for the inlet pressure.

Key Concepts

Pressure Conversions

When working with different units of pressure, it's crucial to understand how to convert between them. This process, known as pressure conversion, is essential in fields like gas chromatography where precision is key. In this context, we dealt with the conversion of pressure from psi (pounds per square inch) in the gauge form (psig) to the absolute form (psi). Pressure can be expressed in several units, such as psi, atm, bar, and torr. Each has its corresponding conversion factor. Here's a simple way to relate some of these units:

• 1 atm = 14.7 psi = 760 torr
• 1 psi = 68.95 torr
• 1 atm = 1013.25 millibar

A systematic approach involves identifying the given unit, converting it to an absolute pressure if necessary, and then leveraging the known conversion factors to move to the desired unit. By doing this, you ensure accurate results during the conversion process.

Gas Reduction Valves

Gas reduction valves play a significant role in controlling the pressure delivered from gas tanks in applications like gas chromatography. These devices are designed to reduce and regulate the high-pressure gas stored in a tank to a much lower and more manageable pressure suitable for the instrument in use. The purpose of the gas reduction valve is to act as a control mechanism, ensuring consistency and safety throughout the experimentation or process. It provides:

• Consistent pressure delivery
• Protection from overpressure conditions
• Enhanced control over the gas flow

In essence, they do not just reduce gas pressure; they also stabilize it, allowing for accurate experimental conditions and reliable results. Ensuring the valve is correctly calibrated for the ambient atmospheric conditions is crucial, as it upholds the precision and general safety of the process.

PSIG to PSI Conversion

The conversion from PSIG (pounds per square inch gauge) to PSI (pounds per square inch absolute) is a common challenge in pressure-related applications, especially when atmospheric conditions are involved. PSIG measures the pressure relative to atmospheric pressure, which means it does not include the atmospheric pressure in its reading.To convert PSIG to PSI, you simply add the atmospheric pressure at the site to the PSIG value. For example, if you have 40.0 PSIG and the atmospheric pressure is approximately 14.42 PSI, then the absolute pressure PSI is calculated as:\[ 40.0 \text{ PSIG} + 14.42 \text{ PSI} = 54.42 \text{ PSI} \]This conversion is crucial for processes sensitive to pressure variations, as many scientific instruments and industrial processes require pressure measurements in absolute terms to ensure they can function accurately and effectively.