Questions: n = (P V) / (R T) * (1.017 atm)(1.0^2 c) / (0.0221 atm/m.k)(3461 t) = 1.03734

Transcript text: $n=\frac{P V}{R T} \frac{(1.017 \mathrm{~atm})\left(1.0^{2} \mathrm{c}\right)}{\left(0.0221 \frac{\mathrm{artm}}{\mathrm{m} \cdot \mathrm{k}}\right)(3461 \mathrm{t})}=1.03734$

Solution

Solution Steps

Step 1: Identify the given variables and constants

We are given the following variables and constants:

Pressure, $ P = 1.017 \, \text{atm} $
Volume, $ V = 1.0^2 \, \text{c} $
Gas constant, $ R = 0.0221 \, \frac{\text{atm}}{\text{m} \cdot \text{K}} $
Temperature, $ T = 3461 \, \text{t} $

Step 2: Substitute the values into the equation

The equation for the number of moles $ n $ is given by: \[ n = \frac{P V}{R T} \] Substituting the given values: \[ n = \frac{(1.017 \, \text{atm}) \left(1.0^2 \, \text{c}\right)}{\left(0.0221 \, \frac{\text{atm}}{\text{m} \cdot \text{K}}\right) (3461 \, \text{t})} \]

Step 3: Simplify the expression

First, calculate the numerator: \[ 1.017 \, \text{atm} \times 1.0^2 \, \text{c} = 1.017 \, \text{atm} \cdot \text{c} \]

Next, calculate the denominator: \[ 0.0221 \, \frac{\text{atm}}{\text{m} \cdot \text{K}} \times 3461 \, \text{t} = 76.6981 \, \frac{\text{atm} \cdot \text{t}}{\text{m} \cdot \text{K}} \]

Now, divide the numerator by the denominator: \[ n = \frac{1.017 \, \text{atm} \cdot \text{c}}{76.6981 \, \frac{\text{atm} \cdot \text{t}}{\text{m} \cdot \text{K}}} \]

Step 4: Calculate the final value

Perform the division: \[ n = \frac{1.017}{76.6981} = 0.0133 \]