To find the density of the gas at Standard Temperature and Pressure (STP) in grams per liter (g/L), we can follow these steps:
### Step 1: Convert the given temperature to Kelvin
The temperature is given as 273°C. To convert Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
So,
\[ T_1 = 273 + 273 = 546 \, K \]
**Hint:** Remember that to convert Celsius to Kelvin, you always add 273.
### Step 2: Identify the given values
We have the following values:
- Pressure \( P_1 = 380 \, \text{torr} \)
- Density \( D_1 = 1.25 \, \text{kg/m}^3 \)
- Temperature \( T_1 = 546 \, K \)
- At STP, \( P_2 = 760 \, \text{torr} \) and \( T_2 = 273 \, K \)
**Hint:** Make sure to note the conditions for STP: 0°C (273 K) and 1 atm (760 torr).
### Step 3: Use the density relation for gases
We can use the formula relating the densities at two different conditions:
\[
\frac{P_1}{D_1 T_1} = \frac{P_2}{D_2 T_2}
\]
Rearranging gives us:
\[
D_2 = \frac{P_2 D_1 T_1}{P_1 T_2}
\]
**Hint:** This formula comes from the ideal gas law and relates pressure, density, and temperature.
### Step 4: Substitute the known values into the equation
Now we substitute the known values into the equation:
\[
D_2 = \frac{760 \, \text{torr} \times 1.25 \, \text{kg/m}^3 \times 546 \, K}{380 \, \text{torr} \times 273 \, K}
\]
**Hint:** Ensure you keep track of units when substituting values.
### Step 5: Calculate \( D_2 \)
Now we perform the calculation:
\[
D_2 = \frac{760 \times 1.25 \times 546}{380 \times 273}
\]
Calculating the numerator:
\[
760 \times 1.25 \times 546 = 1,033,500
\]
Calculating the denominator:
\[
380 \times 273 = 103,740
\]
Now, divide the two results:
\[
D_2 = \frac{1,033,500}{103,740} \approx 9.95 \, \text{kg/m}^3
\]
**Hint:** Double-check your arithmetic to ensure accuracy.
### Step 6: Convert \( D_2 \) to g/L
To convert from kg/m³ to g/L, we use the conversion:
1 kg/m³ = 1 g/L. Thus:
\[
D_2 \approx 9.95 \, \text{g/L}
\]
**Hint:** Remember that 1 kg/m³ is equivalent to 1 g/L.
### Final Answer
The density of the gas at STP is approximately:
\[
\boxed{9.95 \, \text{g/L}}
\]
