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To solve this problem, we need to calculate the pressure at which oxygen has a given density using the Ideal Gas Law. The relevant information provided is:

- Molar mass of oxygen (\( M = 32.00 \, \text{g/mol} \))
- Density (\( d = 1.98 \, \text{g/L} \))
- Temperature (\( T = 20.1^\circ \text{C} \) or \( T = 293.1 \, \text{K} \))
- Gas constant (\( R = 0.08206 \, \text{L atm} / \text{mol K} \))

### Step-by-Step Solution

The Ideal Gas Law \( PV = nRT \) can be adapted to incorporate density. We start from the modified formula given in your notes:

\[
P = \frac{d \cdot R \cdot T}{M}
\]

where:
- \( P \) is the pressure,
- \( d \) is the density,
- \( R \) is the gas constant,
- \( T \) is the temperature in Kelvin,
- \( M \) is the molar mass of the gas.

#### Step 1: Convert Temperature to Kelvin
Given:
\[
T = 20.1^\circ \text{C} = 20.1 + 273.15 = 293.1 \, \text{K}
\]

#### Step 2: Substitute Values into the Formula
Using the values provided:
\[
P = \frac{(1.98 \, \text{g/L}) \times (0.08206 \, \text{L atm} / \text{mol K}) \times (293.1 \, \text{K})}{32.00 \, \text{g/mol}}
\]

#### Step 3: Calculate

1. First, calculate the numerator: \( 1.98 \times 0.08206 \times 293.1 \approx 47.52 \).
2. Divide by the molar mass: \( P = \frac{47.52}{32.00} \approx 1.485 \, \text{atm} \).

### Final Answer
The pressure \( P \) is approximately:
\[
P = 1.49 \, \text{atm} \quad (\text{rounded to 3 significant figures})
\]

Would you like further details on this calculation or have any questions?

Here are five related questions to expand your understanding:
1. How would the pressure change if the temperature increased to 30°C?


Calculate the pressure at which oxygen (32.00) has a density of 1.98 g/L at 20.1°C. (R = 0.08206 L*atm/mol*K)

Learn how to calculate the pressure at which oxygen gas has a density of 1.98 g/L at 20.1°C using the Ideal Gas Law. This solution covers key concepts such as density, pressure calculation, and the use of the Ideal Gas Law formula. Suitable for college-level chemistry students or advanced high school chemistry.

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