give answer in 3 steps with explanation at the end of each step and final answer at the end‘The binding of molecules in the gas phase 10 a sod surface s important in Catalysis and chromatography If we

Question

give answer in 3 steps with explanation at the end of each step and final answer at the end‘The binding of molecules in the gas phase 10 a sod surface s important in Catalysis and chromatography If we designate the.
ecules nh ga 85 A and he traced sufac a 5. the hs “dng” acusbrum fs A) 1S ++ SA whore SA
{woresents tac coogsed byte decd Amolecues For is bldg equllbu he acrpton equdon fs: ¥ = 125,
hic is cad he Langu squion. I he Langu austin, he volume of gas adsorbed ono th surface and Vs he
cme of gas adsrbed whch 08U 1 anclayer COV, 0 Complete Coverage of he sua by a ayer of olecules Acne
ecu hick Ao, P14 he prossurs areried by he 9a ri he fac a AAU and Py 4h eq Br presse
whan haf th surfaces covered. whch occurs when fp = 1 =
Panta
In std of gas ackcrpton cr sok sufacs, the volume of adsorbed ga Vs measured ssa uncton of he proses P.
Which oquaton 3 nearize om of he Langu ecuaton that woukd allow you 0 ban Vr, and Po fom the ope and
inercops?
ASwER
ako =v.y=}
Fe-kthie=vou=}
PVVaP RV 2=V.y=PV
$= iz=Py=§
Parts
Th olin oC a dtc re sched hr moc wa chard econ oO presse
donee
Pum 0m om om osm
Viet 0 oxo ove owe
sigur anes in tA, ma lt of he serpin sn. From ho bu g

VIPSolutions · Accepted Answer

Let's solve this step by step, as requested. We'll break down the problem into three steps and explain each part:

---

### **Step 1: Identify the Correct Linearized Langmuir Equation (Part A)**

**Explanation:**
The Langmuir adsorption isotherm is:

$$
V = \frac{V_m P}{P_0 + P}
$$

To linearize, rearrange in a format $ y = mx + b $:

$$
\frac{P}{V} = \frac{P_0}{V_m} + \frac{P}{V_m}
$$

So, if you plot $\frac{P}{V}$ (y-axis) vs $P$ (x-axis), the slope is $\frac{1}{V_m}$ and y-intercept is $\frac{P_0}{V_m}$.

**Final answer for Step 1 (Part A):**
The correct linearized form is:

$$
\frac{P}{V} = \frac{P_0}{V_m} + \frac{P}{V_m}
$$

---

### **Step 2: Plot the Data and Find Slope and Intercept (Parts B & C)**

**Explanation:**
Now, using the data:

| P (atm) | V (mL) | P/V (atm/mL) |
|---------|--------|--------------|
| 0.132   | 0.128  | 1.031        |
| 0.264   | 0.150  | 1.760        |
| 0.396   | 0.160  | 2.475        |
| 0.528   | 0.166  | 3.181        |

Plot $P/V$ (y-axis) vs $P$ (x-axis). Fit a straight line: $y = mx + b$.

You can use any graphing tool or calculate slope and intercept manually:

- Slope, $m = \frac{\Delta y}{\Delta x}$
- Intercept, $b = y - mx$ (for any point)

Let's use the first and last points for a quick estimation:

$$
\text{Slope} = \frac{3.181 - 1.031}{0.528 - 0.132} = \frac{2.15}{0.396} \approx 5.43 \ \text{atm}^{-1}\text{mL}^{-1}
$$

$$
\text{Intercept} = 1.031 - (5.43 \times 0.132) = 1.031 - 0.717 = 0.314 \ \text{atm mL}^{-1}
$$

**Final answer for Step 2 (Parts B & C):**
- Slope: **5.43 atm$^{-1}$ mL$^{-1}$**
- Y-intercept: **0.314 atm mL$^{-1}$**

---

### **Step 3: Calculate $P_0$, $V_m$, and Volume at $P = 1$ atm (Parts D, E, F)**

**Explanation:**
From the linear form:

- Slope = $1/V_m$ ⇒ $V_m = 1/\text{slope}$
- Intercept = $P_0/V_m$ ⇒ $P_0 = \text{intercept} \times V_m$

Calculate $V_m$:

$$
V_m = \frac{1}{5.43} = 0.184 \ \text{mL}
$$

Calculate $P_0$:

$$
P_0 = 0.314 \times 0.184 = 0.0578 \ \text{atm}
$$

Now, calculate $V$ at $P = 1$ atm using the Langmuir equation:

$$
V = \frac{V_m P}{P_0 + P} = \frac{0.184 \times 1}{0.0578 + 1} = \frac{0.184}{1.0578} = 0.174 \ \text{mL}
$$

**Final answer for Step 3 (Parts D, E, F):**
- $P_0 = 0.0578$ atm
- $V_m = 0.184$ mL
- At $P = 1$ atm, $V = 0.174$ mL

---

## **Summary Table**

| Step | Value | Explanation |
|------|-------|-------------|
| 1    | $\frac{P}{V} = \frac{P_0}{V_m} + \frac{P}{V_m}$ | Linearized Langmuir equation |
| 2    | Slope: 5.43 atm$^{-1}$mL$^{-1}$Intercept: 0.314 atm mL$^{-1}$ | From plot of $P/V$ vs $P$ |
| 3    | $P_0 = 0.0578$ atm$V_m = 0.184$ mL$V_{P=1} = 0.174$ mL | Using results in Langmuir equation |

Let me know if you need the plot or more detailed calculations!

✨ VIPSolutions

Question:

Final Answer:

📢 Instructions:

Study Help, Fast Answers

✨ VIPSolutions

Question:

Final Answer:

📢 Instructions:

Related Answers

Study Help, Fast Answers