Question

A 17.50 liter sealed jar at 78 °C contains a total of 0.95 moles of gas. What is the pressure in the container?

a
0.684 atm
b
0.398 atm
c
0.796 atm
d
1.56 atm

Answer 1

To find the pressure in the container, we can use the Ideal Gas Law, which is given by the formula:

\[ PV = nRT \]

Where:
- \( P \) = pressure (in atm)
- \( V \) = volume (in liters)
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant = 0.0821 L·atm/(K·mol)
- \( T \) = temperature (in Kelvin)

First, we need to convert the temperature from Celsius to Kelvin:

\[
T(K) = T(°C) + 273.15 = 78 + 273.15 = 351.15 \, K
\]

Now we can substitute the values into the Ideal Gas Law:

- \( V = 17.50 \, L \)
- \( n = 0.95 \, moles \)
- \( R = 0.0821 \, L·atm/(K·mol) \)
- \( T = 351.15 \, K \)

Now plug them into the equation:

\[
P \cdot 17.50 = 0.95 \cdot 0.0821 \cdot 351.15
\]

Calculating the right side:

\[
P \cdot 17.50 = 0.95 \cdot 0.0821 \cdot 351.15 \approx 23.1481
\]

Now, to find \( P \):

\[
P = \frac{23.1481}{17.50} \approx 1.32 \, atm
\]

Since this does not match any of the provided choices, let's recalculate by confirming each step:

1. Calculate \( 0.95 \cdot 0.0821 \):
\[
0.95 \cdot 0.0821 \approx 0.078495
\]

2. Now multiply by \( 351.15 \):
\[
0.078495 \cdot 351.15 \approx 27.5636
\]

3. Finally divide by \( 17.50 \):
\[
P = \frac{27.5636}{17.50} \approx 1.57 \, atm
\]

It looks like I made a miscalculation at the first calculation. The closest correct pressure should relate more closely to the final values calculated.

None of the values provided in the multiple-choice are exact due to various approximation errors in the initial calculations. The approximate pressure is closest to **d**, 1.56 atm after proper rounding and match to realistic options.

So the answer you should select is:

**d. 1.56 atm**