A sample of gas has a volume of 240. L at 4.00 atm of pressure and a temperature of 1091K. What is the volume at STP?

Question

Avery Adams · Accepted Answer

#"Volume = 240.219981669L"#

Remember the law regarding gas

#PV = nRT#

Finding moles of gas is the first step in calculating its volume at STP.

Thus, gas moles or n =

#n = (PV)/(RT)#

Utilize the formula to solve the equation.

#n = "(4atm * 240L)"/"(0.0821L * 1091K)"#

#n = 960/89.5711"#

#n = 10.7177426648mol#

Any gas's volume at 1 mole equals 22.4 liters.

Therefore volume of #10.7177426648"moles"# #= 10.7177426648"moles" * 22.4134L = 240.219981669#

But let's continue to demonstrate it.

Volume of 10.7177426648moles in STP Temperature at STP = #0^oC or 273K# Pressure at #STP = 1atm#

#V = 10.7177426648 * 0.0821 * "273K"/"1atm"#

#V = 240.219981669/"1atm"#

#"Volume = 240.219981669L"#

Wyatt Adkins · Answer

undefined Use the ideal gas law equation: $V_1/T_1 = V_2/T_2$.
Rearrange it to find the final volume ($V_2$): $V_2 = V_1 * (T_2/T_1)$.
Convert temperatures to Kelvin.
Plug in values and calculate: $V_2 = 240. L * (273 K / 1091 K)$.

HIX Tutor · Answer

undefined To find the volume of gas at STP (Standard Temperature and Pressure), we can use the Ideal Gas Law and the combined gas law. But let's do it step-by-step.

1. **Understand STP**: STP is 0°C (273 K) and 1 atm pressure.

2. **Use the Ideal Gas Law**: We need to use the formula:
   $$\frac{P_1 \cdot V_1}{T_1} = \frac{P_2 \cdot V_2}{T_2}$$
   Where:
   - $P_1 = 4.00 \text{ atm}$ (initial pressure)
   - $V_1 = 240 \text{ L}$ (initial volume)
   - $T_1 = 1091 \text{ K}$ (initial temperature)
   - $P_2 = 1 \text{ atm}$ (STP pressure)
   - $T_2 = 273 \text{ K}$ (STP temperature)
   - $V_2$ is the volume we want to find.

3. **Plug the numbers into the formula**:
   $$
   \frac{4.00 \cdot 240}{1091} = \frac{1.00 \cdot V_2}{273}
   $$

4. **Cross-multiply to solve for $V_2$**:
   $$
   4.00 \cdot 240 \cdot 273 = 1.00 \cdot V_2 \cdot 1091
   $$

5. **Calculate $V_2$**:
   - First, calculate $4.00 \cdot 240 \cdot 273$:
     $$
     4.00 \cdot 240 = 960
     $$
     Now,
     $$
     960 \cdot 273 = 261120
     $$

- Next, solve for $V_2$:
     $$
     V_2 = \frac{261120}{1091}
     $$

- Finally, calculate $V_2$:
     $$
     V_2 \approx 239.5
     $$

6. **Final Answer**: The volume at STP is **about 239.5 L**.