Calculate the density of helium gas (in g/L) at 778 mm Hg and 34.9 °C.

To calculate the density of helium gas at the given conditions, we can use the **Ideal Gas Law**:  
\[
PV = nRT
\]
where:  
- \(P\) is the pressure (in atm)  
- \(V\) is the volume (in liters)  
- \(n\) is the number of moles  
- \(R\) is the ideal gas constant (0.0821 L·atm/(mol·K))  
- \(T\) is the temperature in Kelvin  

Since density (\(\rho\)) is defined as:
\[
\rho = \frac{\text{mass}}{\text{volume}} = \frac{n \cdot M}{V}
\]
where \(M\) is the molar mass of helium (4.0026 g/mol), we rearrange the Ideal Gas Law to express density directly:
\[
\rho = \frac{PM}{RT}
\]

---

### Step 1: Convert Pressure to atm  
Since the gas constant \(R\) uses atm, we need to convert the given pressure from mmHg to atm:  
\[
P = \frac{778 \, \text{mmHg}}{760 \, \text{mmHg/atm}} = 1.0237 \, \text{atm}
\]

---

### Step 2: Convert Temperature to Kelvin  
\[
T = 34.9^\circ C + 273.15 = 308.05 \, K
\]

---

### Step 3: Calculate the Density  
Now we substitute the values into the density formula:
\[
\rho = \frac{(1.0237 \, \text{atm}) \cdot (4.0026 \, \text{g/mol})}{(0.0821 \, \text{L·atm/(mol·K)}) \cdot (308.05 \, K)}
\]

Evaluating:
\[
\rho = \frac{4.097 \, \text{g·atm/mol}}{25.33 \, \text{L·K/mol}} = 0.1617 \, \text{g/L}
\]

---

### Final Answer  
The density of helium gas at 778 mm Hg and 34.9 °C is:
\[
\boxed{0.1617 \, \text{g/L}}
\]

---

Do you have any questions or need further clarification?  

### Related Questions:
1. How does the density of helium change with increasing temperature?
2. What is the density of helium at STP (0°C and 1 atm)?
3. How do other noble gases' densities compare to helium under the same conditions?
4. What assumptions are made when using the Ideal Gas Law for calculating gas densities?
5. How would the density change if the gas were compressed to a higher pressure?

**Tip:** Always convert temperature to Kelvin when using the Ideal Gas Law to avoid calculation errors.

Learn how to calculate the density of helium gas at 778 mm Hg and 34.9 °C using the Ideal Gas Law. This step-by-step guide covers pressure and temperature conversions and density calculation with detailed explanations. Ideal for high school chemistry students.

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