Question

A tank of acetylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) contains \(48.5 \mathrm{lb}\) of the gas and is at a pressure of \(600.2 \mathrm{lb} / \mathrm{in} .^{2}\) Express the pressure of the gas in atmospheres and the amount of gas in moles. \([760.0 \mathrm{~mm} \mathrm{Hg}=\) \(\left.14.696 \mathrm{lb} / \mathrm{in} .^{2}, 453.6 \mathrm{~g}=1 \mathrm{lb}\right]\)

Short answer

The pressure of the acetylene gas is approximately \(30.93 \, \mathrm{mm \, Hg}\), and there are about \(846.14 \, \mathrm{mol}\) of the gas in the tank.

Step-by-step solution

Convert pressure to atmospheres

To convert the pressure of the gas from lb/in^2 to atmospheres (atm), we'll use the conversion factor given in the problem: 760.0 mm Hg = 14.696 lb/in^2. To do this, we'll set up a proportion like this: \[ \frac{600.2 \, \mathrm{lb/in^{2}}}{14.696 \, \mathrm{lb/in^{2}}} = \frac{x}{760.0 \, \mathrm{mm \, Hg}} \] Now, solve for x: \[ x = \frac{600.2 \, \mathrm{lb/in^{2}} \cdot 760.0 \, \mathrm{mm \, Hg}}{14.696 \, \mathrm{lb/in^{2}}} \] Calculating x, we get: \[ x ≈ 30.93 \, \mathrm{mm \, Hg} \] So, the pressure in atmospheres is approximately \(30.93 \, \mathrm{mm \, Hg}\).

Convert gas amount to moles

Now, we need to convert the amount of gas from pounds to moles. First, we'll convert from pounds to grams using the conversion rate 453.6 g = 1 lb: \[ 48.5 \, \mathrm{lb} \cdot \frac{453.6 \, \mathrm{g}}{1 \, \mathrm{lb}} = 21999.6 \, \mathrm{g} \] Next, we'll convert from grams to moles using the molecular weight of C2H2 (approximately 26 g/mol): \[ 21999.6 \, \mathrm{g} \cdot \frac{1 \, \mathrm{mol}}{26 \, \mathrm{g}} ≈ 846.14 \, \mathrm{mol} \] So, there are approximately \(846.14 \, \mathrm{mol}\) of acetylene gas in the tank.

Key concepts

Atmospheric Pressure

Atmospheric Pressure is a key concept in the study of gases and is crucial when converting between different units of pressure. It is defined as the force exerted by the weight of the atmosphere over a particular area. The standard atmospheric pressure is often considered to be 760.0 mm Hg (millimeters of mercury).

When converting gas pressure to atmospheric units, such as from pounds per square inch (lb/in²) to atmospheres (atm), we utilize given conversion factors. For example, the given conversion factor in this exercise is that 1 atmosphere equals 14.696 lb/in². To convert pressure from lb/in² to atm, you use a proportion where you divide the pressure in lb/in² by the conversion factor. This allows us to understand pressure using a more universal unit, atmosphere, which is widely used in scientific contexts.

Pressure conversions are essential in many scientific calculations, as they allow comparisons and standardizations across different measurement systems. This step is particularly important in fields like chemistry and physics, where observations and predictions depend heavily on accurate pressure readings.

Moles Conversion

Moles Conversion is a fundamental process in chemistry used to quantify the amount of a substance. The mole is a basic unit in the International System of Units (SI), used to measure the amount of a substance. It relates to the number of atoms, ions, or molecules present in a sample.

To convert the mass of a substance to moles, we need to use the substance's molecular weight as a conversion factor. For instance, in our exercise, we deal with acetylene gas \(\mathrm{C}_{2}\mathrm{H}_{2}\). First, convert the mass from pounds (a more commonly used unit in daily life) to grams using the conversion factor where 1 lb equals 453.6 g. Once we have the mass in grams, we determine moles by dividing the mass by the molecular weight (in this case, the molecular weight of acetylene, which is approximately 26 g/mol).

Understanding how to convert mass into moles helps in predicting how substances will react and interact, which is crucial for practical applications like creating chemical solutions, balancing chemical equations, and conducting experiments in the lab.

Molecular Weight Calculation

Molecular Weight Calculation is an essential tool when working with chemical equations and reactions. This calculated weight is typically measured in grams per mole (g/mol) and provides critical information about how substances will behave in chemical processes.

To calculate the molecular weight of a compound, you add up the atomic masses of all the atoms in a molecule. Take acetylene \(\mathrm{C}_{2}\mathrm{H}_{2}\), for example, which consists of two carbon atoms and two hydrogen atoms. The atomic mass of carbon is approximately 12 g/mol and that of hydrogen is about 1 g/mol. Therefore, the molecular weight of acetylene is calculated as follows: \(2 \times 12 + 2 \times 1 = 26 \text{ g/mol}\).

Having the molecular weight allows you to convert masses of substances to moles, which then helps to determine the stoichiometry of reactions. This is crucial for everything from classroom experiments to large-scale industrial chemical production. Understanding molecular weight helps predict how much of a reactant is needed to produce a desired amount of product, making it a cornerstone of chemical calculations.