**Problem Analysis:**
In this problem, we are given that a sample of HI is 22% dissociated at equilibrium. We are then asked to determine the degree of dissociation if hydrogen is added in the proportion of 1 mole for every mole of HI originally present, while keeping the temperature and volume constant.

**Solution:**
To solve this problem, we need to consider the balanced chemical equation for the dissociation of HI:

2 HI ⇌ H2 + I2

Let's assume that initially we have 1 mole of HI. At equilibrium, 22% of HI dissociates, which means that 0.22 moles of HI have dissociated and formed 0.22 moles of H2 and 0.22 moles of I2.

**Step 1: Calculate the moles of HI remaining:**
Initially, we have 1 mole of HI. Since 0.22 moles of HI have dissociated, the moles of HI remaining at equilibrium is:
1 mole - 0.22 moles = 0.78 moles

**Step 2: Calculate the moles of H2 formed:**
Since 0.22 moles of HI have dissociated, the moles of H2 formed at equilibrium is also 0.22 moles.

**Step 3: Calculate the total moles of H2 after addition:**
According to the given condition, for every mole of HI originally present, 1 mole of H2 is added. Since initially, we had 1 mole of HI, we add 1 mole of H2. Therefore, the total moles of H2 after addition is:
0.22 moles (formed during dissociation) + 1 mole (added) = 1.22 moles

**Step 4: Calculate the new moles of HI at equilibrium:**
Since 1 mole of H2 is added for every mole of HI originally present, the new moles of HI at equilibrium is:
0.78 moles (remaining HI) + 1 mole (added H2) = 1.78 moles

**Step 5: Calculate the degree of dissociation:**
The degree of dissociation is defined as the moles of HI dissociated divided by the initial moles of HI. Therefore, the degree of dissociation is:
0.22 moles (dissociated HI) / 1 mole (initial HI) = 0.22

**Step 6: Calculate the new degree of dissociation:**
To determine the new degree of dissociation, we need to calculate the moles of HI dissociated after the addition of hydrogen. Since 0.22 moles of HI dissociated initially, and 1 mole of H2 is added, the new moles of HI dissociated is:
0.22 moles (initial dissociation) + 1 mole (added H2) = 1.22 moles

Now, we can calculate the new degree of dissociation by dividing the new moles of HI dissociated by the new moles of HI:
1.22 moles (dissociated HI) / 1.78 moles (new HI) = 0.685

Converting this to a percentage, we get:
0.685 * 100 = 68.5%

Therefore, the new degree of dissociation is 68.